Since its introduction by Felix Hausdorff in 1919, the concept of the Hausdorff dimension of sets and measures has been a versatile and powerful tool in classical analysis, geometry and geometric measure theory, mathematical physics and their numerous applications. However, there has been a particularly important symbiosis between dynamical systems and dimension theory. This connection arises both from application of dimension theory to the classification and geometric analysis of dynamical systems (and their invariant sets and measures), and the fact that many classical objects of study in mathematics arise from (sometimes implicit) dynamical systems, which often play a role in the dimension theory of said objects.
Recently, there has been substantial progress on a number of central problems in dimension theory, and while many old problems remain, many new ones have also presented themselves. These include a deeper understanding of the relationship between dimension, entropy and Lyapunov exponents; the recent strengthenings of the Marstrand projection theorem and its implications for dimensions of sums of Cantor sets and the connections with number theory; multifractal analysis of ergodic averages, particularly the recent advances for multiple ergodic averages; and improved computational methods for obtaining effective bounds on Hausdorff dimension. This proposed program aims to set the stage for further progress on the many open problems in the field.
It is a challenging classical problem to compute numerically dimensions of given fractals. In recent years, computer-aided proofs in mathematical analysis have gained an increasing presence in mathematical research. One reason for this field's growing impact is due to its ability to produce high-quality quantitative information about global, nonlinear problems. As a consequence, solutions to a large class of previously intractable problems are now within reach and recently several long-standing conjectures have been verified using rigorous computations.
During the semester we will focus on three specific aspects of the interaction between these two areas: (i) Ergodic, algebraic and combinatorial methods in dimension theory (ii) Computations in fractal geometry in dynamical systems; and (iii) Fractal geometry and hyperbolic dynamics.
Photo Credit: Mark A. Wilson
Mini-Courses
A class of random Cantor measures, with applications - Pablo Shmerkin, Universidad Torcuato Di Tella
Schmidt games and fractals in dynamics and number theory - Barak Weiss, Tel Aviv University
Schmidt games and fractals in dynamics and number theory - Dmitry Kleinbock, Brandeis UniversityEquidistribution and dimension via additive combinatorics - Elon Lindenstrauss, The Hebrew University of Jerusalem
Symbolic dynamics for hyperbolic systems - Yuri Lima, University of Paris
Microlocal techniques for hyperbolic dynamics - Semyon Dyatlov, MIT
Multifractal analysis, large deviations and Fourier transforms for countable branch expanding maps - Thomas Jordan, University of Bristol
Béla Barabás, Ottilia Fülöp, Roland Molontay, Gyula Pályi, Impact of the discovery of fluorous biphasic systems on chemistry: A statistical and network analysis, ACS Sustainable Chemistry \& Engineering 5 (2017) no. 9, 8108-8118.
Mayer Humi, John Roumas, Structure of polytropic stars in General Relativity, Astrophysics and Space Science 364 (2019) no. 7.
Kyle Hambrook, Krystal Taylor, Measure and dimension of sums and products, Proc. Amer. Math. Soc. 149 (2021) no. 9, 3765-3780.
Ill{\'e}s Horv{\'a}th, Istv{\'a}n Finta, Ferenc Kov{\'a}cs, Andr{\'a}s M{\'e}sz{\'a}ros, Roland Molontay, Kriszti{\'a}n Varga, Markovian queue with garbage collection, International Conference on Analytical and Stochastic Modeling Techniques and Applications, Springer, 2017, pp. 109-124.
Attila Egri, Ill{\'e}s Horv{\'a}th, Ferenc Kov{\'a}cs, Roland Molontay, Kriszti{\'a}n Varga, Cross-correlation based clustering and dimension reduction of multivariate time series, 2017 IEEE 21st International Conference on Intelligent Engineering Systems (INES), IEEE, 2017, pp. 000241-000246.
Martina Z{\""a}hle, Erik Schneider, Forward integrals and SDE with fractal noise, Horizons of fractal geometry and complex dimensions 731 (2019), 279-302.
Lorenzo J. D'iaz, Katrin Gelfert, Maik Groger, Tobias Jager, Hyperbolic graphs: Critical regularity and box dimension, Transactions of the American Mathematical Society (2019).
Katrin Gelfert, Daniela Oliveira, Invariant multi-graphs in step skew-products, Dynamical Systems 35 (2019), 1 - 28.
Pablo Shmerkin, \$\$L^q\$\$ Dimensions of Self-similar Measures and Applications: A Survey, New Trends in Applied Harmonic Analysis, Volume 2 (2019).
Jialu Fang, Yongluo Cao, Yun Zhao, Measure theoretic pressure and dimension formula for non-ergodic measures, Discrete \& Continuous Dynamical Systems - A (2020).
Nishant Chandgotia, Brian Marcus, Mixing properties for hom-shifts and the distance between walks on associated graphs, Pacific Journal of Mathematics 294 (2018) no. 1, 41–69.
Daniel Coronel, Cristobal Rojas, Michael Yampolsky, Non computable Mandelbrot-like sets for a one-parameter complex family, Inf. Comput. 262 (2018), 110-122.
Renato Calleja, Marta Canadell, Alex Haro, Non-twist invariant circles in conformally symplectic systems, Communications in Nonlinear Science and Numerical Simulation 96 (2021), 105695.
Pablo Shmerkin, On Furstenberg's intersection conjecture, self-similar measures, and the Lq norms of convolutions, Annals of Mathematics (2019).
Péter Bálint, Thomas Gilbert, Péter Nándori, Domokos Szász, Imre Péter Tóth, On the Limiting Markov Process of Energy Exchanges in a Rarely Interacting Ball-Piston Gas, Journal of Statistical Physics 166 (2016) no. 3-4, 903–925.
Yuanyang Chang, Min Wu, Wen Wu, Quantitative recurrence properties and homogeneous self-similar sets, Proceedings of the American Mathematical Society (2018).
Katrin Gelfert, Örjan Stenflo, Random iterations of homeomorphisms on the circle, Modern Stochastics: Theory and Applications 4 (2017) no. 3, 253–271.
Cristobal Rojas, Michael Yampolsky, Real Quadratic Julia Sets Can Have Arbitrarily High Complexity, Foundations of Computational Mathematics 21 (2021), 59-69.
Denis Gaidashev, Remus Radu, Michael Yampolsky, Renormalization and Siegel disks for complex H\'enon maps, J. Eur. Math. Soc. (JEMS) 23 (2021) no. 4, 1053-1073.
Warwick Tucker, \it Rigorous numerics in dynamics [book review of
MR3822720], SIAM Rev. 62 (2020) no. 2, 524-526.
P. Pilarczyk, S. Luzzatto, Rigorous computation of escape times for parameter intervals in the quadratic map, 2021.
Zbigniew Galias, Warwick Tucker, Rigorous integration of smooth vector fields around spiral saddles with an application to the cubic Chua's attractor, Journal of Differential Equations 266 (2019) no. 5, 2408-2434.
A. Golmakani, C. E. Koudjinan, S. Luzzatto, P. Pilarczyk, Rigorous numerics for critical orbits in the quadratic family, Chaos: An Interdisciplinary Journal of Nonlinear Science 30 (2020) no. 7, 073143.
'Abel Farkas, Jonathan M Fraser, Erez Nesharim, David Simmons, SCHMIDT'S GAME ON HAUSDORFF METRIC AND FUNCTION SPACES: GENERIC DIMENSION OF SETS AND IMAGES, Mathematika (2020).
Yakov Pesin, Sinai's Work on Markov Partitions and SRB Measures, Springer International Publishing, Cham, 2019.
Koji Sato, Ryokichi Tanaka, Solitons in one-dimensional mechanical linkage, Physical Review E 98 (2018) no. 1.
Vaughn Climenhaga, Stefano Luzzatto, Yakov Pesin, SRB Measures and Young Towers for Surface Diffeomorphisms, Annales Henri Poincar{\'e} (2021).
Michael Yampolsky, Jonguk Yang, The Boundaries of Golden-Mean Siegel Disks in the Complex Quadratic H\'enon Family Are Not Smooth, New Trends in One-Dimensional Dynamics (2019).
JIANYU CHEN, HUYI HU, YAKOV PESIN, KE ZHANG, The essential coexistence phenomenon in Hamiltonian dynamics, Ergodic Theory and Dynamical Systems (2021), 1–22.
Martina Zähle, The Mean Minkowski Content of Homogeneous Random Fractals, Mathematics 8 (2020) no. 6.
Y. PESIN, S. SENTI, K. ZHANG, Thermodynamics of the Katok map, Ergodic Theory and Dynamical Systems 39 (2017) no. 3, 764–794.
RYOKICHI TANAKA, Topological flows for hyperbolic groups, Ergodic Theory and Dynamical Systems (2020), 1–47.
Júlia Komjáthy, Roland Molontay, Károly Simon, Transfinite fractal dimension of trees and hierarchical scale-free graphs, Journal of Complex Networks 7 (2019) no. 5, 764–791.
Keith Burns, Vaughn Climenhaga, Todd Fisher, Daniel J. Thompson, Unique equilibrium states for geodesic flows in nonpositive curvature, Geometric and Functional Analysis 28 (2017), 1209-1259.
T. Tsutsumi, Yuriko Ono, Z. Arai, T. Taketsugu, Visualization of dynamics effect: projection of on-the-fly trajectories to the subspace spanned by the static reaction path network., Journal of chemical theory and computation (2020).
Pedro Birindiba, Katrin Gelfert, When winning sets have full dimension, Involve: A Journal of Mathematics 14 (2021) no. 2, 195 - 207.
Ian D. Morris, Pablo Shmerkin, On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems, arXiv 1602.08789 (2016).
Izabella Laba, Maximal operators and decoupling for \$\Lambda(p)\$ Cantor measures, arXiv 1808.05657 (2018).
M. Benedicks, M. Martens, L. Palmisano, Newhouse Laminations., arXiv 1811.00617 (2018).
Artem Dudko, Michael Yampolsky, On computational complexity of Cremer Julia sets, arXiv 1907.11047 (2019).
Eino Rossi, Pablo Shmerkin, On measures that improve \$L^q\$ dimension under convolution, arXiv 1812.05660 (2018).
Zin Arai, Yutaka Ishii, On parameter loci of the H\'enon family., arXiv 1501.01368 (2015).
Vaughn Climenhaga, SRB and equilibrium measures via dimension theory, arXiv 2009.09260 (2020).
Laura Cladek, Blair Davey, Krystal Taylor, Upper and lower bounds on the rate of decay of the Favard curve length for the four-corner Cantor set, arXiv 2003.03620 (2020).
P'eter B'alint, Thomas Gilbert, Domokos Sz'asz, Imre P'eter T'oth, What mathematical billiards teach us about statistical physics, arXiv 2009.06284 (2020).
Yuanyang Chang, Min Wu, Wen Wu, Quantitative recurrence properties and homogeneous self-similar sets, Proceedings of the American Mathematical Society (2018).
Wael Bahsoun, Christopher J. Bose, Marks Ruziboev, Quenched decay of correlations for slowly mixing systems, Transactions of the American Mathematical Society (2019).
Laura Cladek, Radial Fourier multipliers in ℝ3 and
ℝ4, Analysis & PDE 11 (2018) no. 2, 467–498.
Katrin Gelfert, Örjan Stenflo, Random iterations of homeomorphisms on the circle, Modern Stochastics: Theory and Applications 4 (2017) no. 3, 253–271.
J{\'e}r{\'e}mie Brieussel, Ryokichi Tanaka, Tianyi Zheng, Random walks on the discrete affine group, Groups, Geometry, and Dynamics (2021).
Guozhen Lu, Qiaohua Yang, Sharp Hardy–Adams inequalities for bi-Laplacian on hyperbolic space of dimension four, Advances in Mathematics 319 (2017), 567-598.
Rafael de la Llave, Simple proofs and extensions of a result of L. D.
Pustylnikov on the nonautonomous Siegel theorem, Regul. Chaotic Dyn. 22 (2017) no. 6, 650-676.
Y. Pesin, Sinai s Work on Markov Partitions and SRB Measures, 2019.
Lorenzo J. D\'{\i}az, Salete Esteves, Jorge Rocha, Skew product cycles with rich dynamics: from totally
non-hyperbolic dynamics to fully prevalent hyperbolicity, Dyn. Syst. 31 (2016) no. 1, 1-40.
Mark F. Demers, Mike Todd, Slow and Fast Escape for Open Intermittent Maps, Communications in Mathematical Physics 351 (2017) no. 2, 775–835.
Mayer Humi, Solutions to Painleve III and other nonlinear equations by a generalized Cole–Hopf transformation, Mathematical Methods in the Applied Sciences 40 (2017) no. 11, 4092-4101.
Jos{\'e} F. Alves, Christian Bonatti, Marcelo Viana, SRB measures for partially hyperbolic systems whose central direction is mostly expanding, Inventiones mathematicae 140 (2000), 351-398.
Alexander I. Bufetov, Boris Solomyak, The H\"older property for the spectrum of translation flows in
genus two, Israel J. Math. 223 (2018) no. 1, 205-259.
Y. PESIN, S. SENTI, K. ZHANG, Thermodynamics of the Katok map, Ergodic Theory and Dynamical Systems 39 (2017) no. 3, 764–794.
Yakov Pesin, Agnieszka Zelerowicz, Yun Zhao, Time rescaling of Lyapunov exponents, Advances in dynamics, patterns, cognition, vol. 20, Springer, Cham, 2017, pp. 29-40.
L. Díaz, Katrin Gelfert, Michal Rams, Topological and ergodic aspects of partially hyperbolic diffeomorphisms and nonhyperbolic step skew products, Proceedings of the Steklov Institute of Mathematics 297 (2017), 98-115.
Rafael de la Llave, Uniform boundedness of iterates of analytic mappings implies
linearization: a simple proof and extensions, Regul. Chaotic Dyn. 23 (2018) no. 1, 1-11.
Laura Cladek, Kevin Henriot, Ben Krause, Izabella Łaba, Malabika Pramanik, A discrete carleson theorem along the primes with a restricted supremum, Mathematische Zeitschrift 289 (2016), 1033-1057.
Lei Jin, Siming Tu, A new universal real flow of the Hilbert-cubical type, Dynamical Systems 34 (2018), 234 - 238.
Artem Dudko, Michael Yampolsky, Almost Every Real Quadratic Polynomial has a Poly-time Computable Julia Set, Foundations of Computational Mathematics 18 (2018), 1233-1243.
L. Marangio, J. Sedro, S. Galatolo, A. Di Garbo, M. Ghil, Arnold Maps with Noise: Differentiability and Non-monotonicity of the Rotation Number, Journal of Statistical Physics 179 (2019) no. 5-6, 1594–1624.
Dmitry Dolgopyat, P'eter N'andori, Franccoise Pene, Asymptotic expansion of correlation functions for \$\mathbb\Z\^d\$ covers of hyperbolic flows, 2019.
M. Benedicks, L. Palmisano, Coexistence phenomena in the H\'enon family, 2018.
Cristobal Rojas, Michael Yampolsky, Computational intractability of attractors in the real quadratic family, Advances in Mathematics (2019).
Jan Rataj, Martina Z\"{a}hle, Curvature measures of singular sets, Springer Monographs in Mathematics, Springer, Cham, 2019.
Yongluo Cao, Yakov Pesin, Yun Zhao, Dimension Estimates for Non-conformal Repellers and Continuity of Sub-additive Topological Pressure, Geometric and Functional Analysis (2019).
Jonathan M Fraser, Thomas Jordan, Natalia Jurga, Dimensions of equilibrium measures on a class of planar self-affine sets, Journal of Fractal Geometry (2019).
Péter Bálint, Péter Nándori, Domokos Szász, Imre Péter Tóth, Equidistribution for Standard Pairs in Planar Dispersing Billiard Flows, Annales Henri Poincaré 19 (2018) no. 4, 979–1042.
Rodrigo Trevi{\~n}o, Equilibrium Configurations for Generalized Frenkel–Kontorova Models on Quasicrystals, Communications in Mathematical Physics (2019).
Vaughn Climenhaga, Yakov Pesin, Agnieszka Zelerowicz, Equilibrium measures for some partially hyperbolic systems, Journal of Modern Dynamics 16 (2020) no. 0, 155–205.
Vaughn Climenhaga, Yakov Pesin, Agnieszka Zelerowicz, Equilibrium states in dynamical systems via geometric measure theory, Bulletin of the American Mathematical Society (2018).
Pablo Shmerkin, Ville Suomala, Patterns in random fractals, arXiv 1703.09553 (2017).
Alex Iosevich, Krystal Taylor, Ignacio Uriarte-Tuero, Pinned Geometric Configurations in Euclidean Space and Riemannian Manifolds, arXiv 1610.00349 (2016).
Dzmitry Badziahin, Stephen Harrap, Erez Nesharim, David Simmons, Schmidt games and Cantor winning sets, arXiv 1804.06499 (2018).
Efrat Bank, Erez Nesharim, Steffen Hojris Pedersen, Solution of Cassels' Problem on a Diophantine Constant over Function Fields, arXiv 1512.07231 (2015).
Franccois Ledrappier, Lin Shu, THE REGULARITY OF THE LINEAR DRIFT IN NEGATIVELY CURVED SPACES, arXiv 1711.02859 (2018).
Chang Shing Chen, Meng Wu, Wen Wu, Accessible Values for the Assouad and Lower Dimensions of Subsets, arXiv 1602.02180 (2016).
Yakov Pesin, Samuel Senti, Farruh Shahidi, Area preserving surface diffeomorphisms with polynomial decay of correlations are ubiquitous, arXiv 2003.08503 (2020).
Izabella Laba, Hong Wang, Decoupling and near-optimal restriction estimates for Cantor sets, arXiv 1607.08302 (2016).
Stefano Galatolo, Maurizio Monge, Isaia Nisoli, Existence of noise induced order, a computer aided proof, arXiv 1702.07024 (2017).
Michael Benedicks, Michal Misiurewicz, Ana Rodrigues, Expansion properties of Double Standard Maps, arXiv 2002.02019 (2020).
Dmitry Dolgopyat, Changguang Dong, Adam Kanigowski, P'eter N'andori, Flexibility of statistical properties for smooth systems satisfying the central limit theorem, arXiv 2006.02191 (2020).
Paweł Pilarczyk, A space-efficient algorithm for computing the minimum cycle mean in a directed graph, Journal of Mathematics and Computer Science 20 (2020) no. 4, 349-355.
Jordi-Llu{\'i}s Figueras, Rafael de la Llave, Numerical Computations and Computer Assisted Proofs of Periodic Orbits of the Kuramoto-Sivashinsky Equation, SIAM J. Appl. Dyn. Syst. 16 (2017), 834-852.
Pablo Shmerkin, On Furstenberg's intersection conjecture, self-similar measures, and the Lq norms of convolutions, Annals of Mathematics (2019).
Xiaotao Lü, Jin Chen, Zhixiong Wen, Wen Wu, On the abelian complexity of the Rudin–Shapiro sequence, Journal of Mathematical Analysis and Applications 451 (2017) no. 2, 822–838.
Michael Hochman, Boris Solomyak, On the dimension of Furstenberg measure for $$ SL_2(\mathbb R)$$ S L 2 ( R ) random matrix products, Inventiones mathematicae 210 (2017) no. 3, 815–875.
Wael Bahsoun, Marks Ruziboev, On the statistical stability of Lorenz attractors with a \$C^\1+\unicode[STIX]\x1D6FC\\\$ stable foliation, Ergodic Theory and Dynamical Systems 39 (2019), 3169 - 3184.
Thomas E. Carter, Mayer Humi, Optimal Planar Impulsive Transfer Using Transformed Variables.
Mayer Humi, John Roumas, Pattern Formation for Isentropic Gas in General Relativity.
Mayer Humi, Patterns Formation in a Self-Gravitating Isentropic Gas, Earth, Moon, and Planets 121 (2018).
Lorenzo J. D{\'i}az, Katrin Gelfert, Michał Rams, Nonhyperbolic step skew-products: Ergodic approximation, arXiv 1602.06845 (2016).
Ian D. Morris, Pablo Shmerkin, On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems, arXiv 1602.08789 (2016).
Jin Chen, Xiaotao L{\"u}, Wen Wu, On the k-abelian complexity of the Cantor sequence, arXiv 1703.04063 (2018).
Jonathan M Fraser, Tom Kempton, On the L^q Dimensions of Measures on Hueter-Lalley Type Self-Affine Sets, arXiv 1607.00894 (2016).
Pablo D. Carrasco, Federico Juan Rodriguez Hertz, Jana Rodriguez Hertz, Ra'ul Ures, Partially hyperbolic dynamics in dimension 3, arXiv 1501.00932 (2015).
Marta Canadell, \`Alex Haro, Computation of quasi-periodic normally hyperbolic invariant
tori: algorithms, numerical explorations and mechanisms of
breakdown, J. Nonlinear Sci. 27 (2017) no. 6, 1829-1868.
Marta Canadell, \`Alex Haro, Computation of quasiperiodic normally hyperbolic invariant
tori: rigorous results, J. Nonlinear Sci. 27 (2017) no. 6, 1869-1904.
Stefano Galatolo, Mark Pollicott, Controlling the statistical properties of expanding maps, Nonlinearity 30 (2017) no. 7, 2737–2751.
K{\'a}roly Simon, Krystal Taylor, Dimension and measure of sums of planar sets and curves, 2017.
RYOKICHI TANAKA, Dimension of harmonic measures in hyperbolic spaces, Ergodic Theory and Dynamical Systems 39 (2017) no. 2, 474–499.
Lifeng Xi, Wen Wu, Ying Xiong, Dimension of slices through fractals with initial cubic
pattern, Chin. Ann. Math. Ser. B 38 (2017) no. 5, 1145-1178.
Sascha Troscheit, Dimension Theory of Random Self-similar and Self-affine Constructions, Ph.D. thesis, 2017.
Jairo Bochi, Christian Bonatti, Katrin Gelfert, Dominated Pesin theory: convex sum of hyperbolic measures, Israel Journal of Mathematics 226 (2015), 387-417.
Lorenzo J. D{\'i}az, Katrin Gelfert, Michał Rams, Entropy Spectrum of Lyapunov Exponents for Nonhyperbolic Step Skew-Products and Elliptic Cocycles, Communications in Mathematical Physics 367 (2019), 351-416.
Rodrigo Trevi{\~n}o, Flat surfaces, Bratteli diagrams and unique ergodicity \`a la Masur, Israel Journal of Mathematics 225 (2016), 35-70.
Lorenzo J. D'iaz, Katrin Gelfert, Maik Groger, Tobias Jager, Hyperbolic graphs: Critical regularity and box dimension, Transactions of the American Mathematical Society (2019).
K{\'a}roly Simon, Krystal Taylor, Interior of sums of planar sets and curves, Mathematical Proceedings of the Cambridge Philosophical Society 168 (2018), 119 - 148.
Qing Hong, Guozhen Lu, Lu Zhang, L p boundedness of rough bi-parameter Fourier integral operators, Forum Mathematicum 30 (2015), 107 - 87.
Marks Ruziboev, Almost sure rates of mixing for random intermittent maps, arXiv 1801.09583 (2017).
Sascha Troscheit, Exact Hausdorff and packing measures for random self-similar code-trees with necks, arXiv 1710.07167 (2017).
Stefano Galatolo, Maurizio Monge, Isaia Nisoli, Existence of noise induced order, a computer aided proof, arXiv 1702.07024 (2017).
Henk Bruin, Mark F. Demers, Mike Todd, Hitting and escaping statistics: mixing, targets and holes, arXiv 1609.01196 (2016).
K{\'a}roly Simon, S'andor Moln'ar, J{\'u}lia Komj{\'a}thy, P'eter M'ora, Large Deviation Multifractal Analysis of a Process Modeling TCP CUBIC, arXiv 1705.11039 (2017).
Wael Bahsoun, Marks Ruziboev, Beno{\^i}t Saussol, Linear response for random dynamical systems, arXiv 1710.03706 (2017).
Jon Chaika, Rodrigo Trevi{\~n}o, Logarithmic laws and unique ergodicity, arXiv 1603.00076 (2016).
Jordi-Llu{\'i}s Figueras, Marcio Gameiro, Jean‐Philippe Lessard, Rafael de la Llave, A Framework for the Numerical Computation and A Posteriori Verification of Invariant Objects of Evolution Equations, SIAM J. Appl. Dyn. Syst. 16 (2017), 1070-1088.
Zeya Mi, Yongluo Cao, Dawei Yang, A note on partially hyperbolic systems with mostly expanding
centers, Proc. Amer. Math. Soc. 145 (2017) no. 12, 5299-5313.
Santiago Saglietti, Pablo Shmerkin, Boris Solomyak, Absolute continuity of non-homogeneous self-similar measures, Advances in Mathematics 335 (2018), 60–110.
Pablo Shmerkin, Ville Suomala, A class of random Cantor measures, with applications, arXiv 1603.08156 (2015).
Jasmina Angelevska, Sascha Troscheit, A dichotomy of self-conformal subsets of the real line with overlaps, arXiv 1602.05821 (2016).
Wael Bahsoun, Stefano Galatolo, Isaia Nisoli, Xiaolong Niu, A Rigorous Computational Approach to Linear Response, arXiv 1506.08661 (2015).
