Computation in Dynamics
(April 4-8, 2016)

Picture
Visualization of a 3D
solenoidal attractor.

Description

Numerical computations have always played an important role in the development of the theory of Differential Equations and Dynamical Systems, more and more so as the availability and power of computers has increased dramatically over the last few decades. At the same time, the limitations of computer-assisted numerical calculations have also become increasingly apparent. Notwithstanding their enormous power, the intrinsic finite resolution of computers can lead to significant errors, especially as a result of a large number of calculations through which small errors can accumulate.

An important and growing approach to certain mathematical problems consists of developing rigorous numerical techniques in combination with more classical analytic methods in order to obtain rigorous qualitative and quantitative results. In some cases this leads to the proof of deep mathematical theorems and in other cases to quantitative, and thus more concrete and applicable, versions of abstract existence results.

This workshop will bring together experts in Dynamical Systems and experts in the theory of Computability to exchange ideas and results, and promote collaborations in view of significant developments in the field over the next few years.

The workshop will include four main streams of research:

  • Approximation of Dynamical Quantities
  • Regular and Stochastic Properties
  • Renormalization
  • Computability in Dynamics

Organizing Committee

= speaker   = poster presenter

Session Chairs:
Monday Morning: Warwick Tucker, Uppsala University
Monday Afternoon: Mark Pollicott, Warwick University
Tuesday Morning: Michael Yampolsky, University of Toronto
Tuesday Afternoon: Piotr Zgliczynski, Jagiellonian University
Wednesday Morning: Denis Gaidashev, Uppsala University
Thursday Morning: Stefano Luzzatto, ITCP-Trieste
Thursday Afternoon: Gary Froyland, University of New South Wales
Friday Morning: Stefano Galatolo, University of Pisa
Friday Afternoon: Jordi-Lluis Figueras, University of Uppsala
Monday April 4, 2016
Time Description Speaker Location Abstracts Slides
8:30 - 8:55Registration11th Floor Collaborative Space
8:55 - 9:00WelcomeICERM Director11th Floor Lecture Hall
9:00 - 9:35Universality for golden mean Siegel disksDenis Gaidashev, Uppsala University11th Floor Lecture Hall
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9:45 - 10:15Coffee/Tea Break11th Floor Collaborative Space
10:15 - 10:50Quasi-periodic solutions for state dependent delay equations.Rafael de la Llave, Georgia Tech11th Floor Lecture Hall
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11:00 - 11:35On the measure of the set of regular parameter values for the quadratic mapZbigniew Galias, AGH University of Science & Technology11th Floor Lecture Hall
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11:45 - 12:00Break
12:00 - 12:35Effective computation of expansivity rates in one-dimensional dynamicsPawel Pilarczyk, IST Austria11th Floor Lecture Hall
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12:45 - 3:00Break for Lunch / Free Time
3:00 - 3:35Linear Response- Formulae and Rigorous ApproximationsWael Bahsoun, Loughborough University11th Floor Lecture Hall
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3:45 - 4:15Coffee/Tea Break11th Floor Collaborative Space
4:15 - 4:50Estimating long-term behavior of periodically driven flows without trajectory integrationGary Froyland, University of New South Wales11th Floor Lecture Hall
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5:00 - 6:30Welcome Reception11th Floor Collaborative Space

Tuesday April 5, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:35Interactive theorem proving, automated reasoning, and dynamical systemsJeremy Avigad, Carnegie Mellon University11th Floor Lecture Hall
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9:45 - 10:15Coffee/Tea Break11th Floor Collaborative Space
10:15 - 10:50Conformal maps- Computability and ComplexityIlia Binder, University of Toronto11th Floor Lecture Hall
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11:00 - 11:35On computational aspects of the Feigenbaum fixed point of the period doubling renormalization.Artem Dudko, Stony Brook University11th Floor Lecture Hall
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11:45 - 12:00Break
12:00 - 12:35Computability and computational complexity in dynamical systems.Cristóbal Rojas, Universidad Andrés Bello (Santiago)11th Floor Lecture Hall
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12:45 - 3:00Break for Lunch / Free Time
3:00 - 3:35Dynamic Signatures Generated by Regulatory NetworksKonstantin Mischaikow, Rutgers University11th Floor Lecture Hall
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3:45 - 4:15Coffee/Tea Break11th Floor Collaborative Space
4:15 - 4:50Conley Index Theory, Symbolic Dynamics, and EntropySarah Day, College of William and Mary11th Floor Lecture Hall
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Wednesday April 6, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:35Stochastic Arnold diffusion of deterministic systemsVadim Kaloshin, University of Maryland11th Floor Lecture Hall
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9:45 - 10:15Coffee/Tea Break11th Floor Collaborative Space
10:15 - 10:50Transition chains of invariant tori around L1 in the Sun-Earth systemPablo Roldán González, Instituto Tecnológico Autónomo de México (ITAM)11th Floor Lecture Hall
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11:00 - 11:35On rigorous verification of the crossed mapping conditionZin Arai, Hokkaido University11th Floor Lecture Hall
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11:45 - 12:00Break
12:00 - 12:35On the bifurcation of hyperbolic invariant manifolds- From Numerics to Rigorous results, and then back to Numerics.Jordi-Lluís Figueras, Uppsala University11th Floor Lecture Hall
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12:45 - 1:00Group Photo in Lecture Hall11th Floor Lecture Hall
1:00 - 3:00Break for Lunch / Free Time
3:00 - 5:00Collaboration and Work Time
3:45 - 4:15Coffee/Tea Break11th Floor Collaborative Space

Thursday April 7, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:35Periodic solutions for some hyperbolic PDEsHans Koch, University of Texas at Austin11th Floor Lecture Hall
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9:45 - 10:15Coffee/Tea Break11th Floor Collaborative Space
10:15 - 10:50Rigorous estimation of the speed of convergence to equilibrium.Stefano Galatolo, University of Pisa11th Floor Lecture Hall
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11:00 - 11:35Introduction to the software package `Dynamics Explorer' for exploration of discrete dynamical systemsSuzanne Lynch Boyd, University of Wisconsin-Milwaukee11th Floor Lecture Hall
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11:45 - 12:00Break
12:00 - 12:35Sharp mixing rates via inducing w.r.t. general return timesDalia Terhesiu, University of Vienna11th Floor Lecture Hall
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12:45 - 3:00Break for Lunch / Free Time
3:00 - 3:35Computer-assisted proofs for periodic orbits of PDEsJean-Philippe Lessard, Université Laval11th Floor Lecture Hall
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3:45 - 4:15Coffee/Tea Break11th Floor Collaborative Space
4:15 - 4:50Set-oriented computation in dynamicsKathrin Padberg-Gehle, Technische Universität Dresden11th Floor Lecture Hall
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Friday April 8, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:35Interval Analysis Methods for Elliptic Boundary Value ProblemsIrina Mitrea, Temple University11th Floor Lecture Hall
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9:45 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:05Rigorous Approximation of stationary Measures and Convergence to Equilbrium for Iterated Function SystemsMaurizio Monge, Federal University of Rio de Janeiro (UFRJ)11th Floor Lecture Hall
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11:15 - 11:50Some practical and theorical issues in computational ergodic theoryIsaia Nisoli, Federal University of Rio de Janeiro (UFRJ)11th Floor Lecture Hall
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12:00 - 12:15Break
12:15 - 12:50Minkowski's question mark function and measure.Giorgio Mantica, Universita' dell'Insubria11th Floor Lecture Hall
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1:00 - 3:00Break for Lunch / Free Time
3:00 - 3:35Melnikov-type method for splitting of separatrices for an explicit range of small parameterPiotr Zgliczynski, Jagiellonian University11th Floor Lecture Hall
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3:45 - 4:15Coffee/Tea Break11th Floor Collaborative Space
4:15 - 4:50Rigorous integration of dissipative PDEs revisited- chaos in the Kuramoto-Sivashinsky equations.Daniel Wilczak, Jagiellonian University11th Floor Lecture Hall
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