Organizing Committee
Abstract

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

Image for "Computation in Dynamics"
Visualization of a 3D solenoidal attractor.

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, April 4, 2016
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration11th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:35am EDTUniversality for golden mean Siegel disks - Denis Gaidashev, Uppsala University11th Floor Lecture Hall
9:45 - 10:15am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:15 - 10:50am EDTQuasi-periodic solutions for state dependent delay equations. - Rafael de la Llave, Georgia Tech11th Floor Lecture Hall
11:00 - 11:35am EDTOn the measure of the set of regular parameter values for the quadratic map - Zbigniew Galias, AGH University of Science & Technology11th Floor Lecture Hall
11:45 - 12:00pm EDTBreak  
12:00 - 12:35pm EDTEffective computation of expansivity rates in one-dimensional dynamics - Pawel Pilarczyk, IST Austria11th Floor Lecture Hall
12:45 - 3:00pm EDTBreak for Lunch / Free Time  
3:00 - 3:35pm EDTLinear Response- Formulae and Rigorous Approximations - Wael Bahsoun, Loughborough University11th Floor Lecture Hall
3:45 - 4:15pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:15 - 4:50pm EDTEstimating long-term behavior of periodically driven flows without trajectory integration - Gary Froyland, University of New South Wales11th Floor Lecture Hall
5:00 - 6:30pm EDTWelcome Reception11th Floor Collaborative Space 
Tuesday, April 5, 2016
TimeEventLocationMaterials
9:00 - 9:35am EDTInteractive theorem proving, automated reasoning, and dynamical systems - Jeremy Avigad, Carnegie Mellon University11th Floor Lecture Hall
9:45 - 10:15am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:15 - 10:50am EDTConformal maps- Computability and Complexity - Ilia Binder, University of Toronto11th Floor Lecture Hall
11:00 - 11:35am EDTOn computational aspects of the Feigenbaum fixed point of the period doubling renormalization. - Artem Dudko, Stony Brook University11th Floor Lecture Hall
11:45 - 12:00pm EDTBreak  
12:00 - 12:35pm EDTComputability and computational complexity in dynamical systems. - Cristóbal Rojas, Universidad Andrés Bello (Santiago)11th Floor Lecture Hall
12:45 - 3:00pm EDTBreak for Lunch / Free Time  
3:00 - 3:35pm EDTDynamic Signatures Generated by Regulatory Networks - Konstantin Mischaikow, Rutgers University11th Floor Lecture Hall
3:45 - 4:15pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:15 - 4:50pm EDTConley Index Theory, Symbolic Dynamics, and Entropy - Sarah Day, College of William and Mary11th Floor Lecture Hall
Wednesday, April 6, 2016
TimeEventLocationMaterials
9:00 - 9:35am EDTStochastic Arnold diffusion of deterministic systems - Vadim Kaloshin, University of Maryland11th Floor Lecture Hall
9:45 - 10:15am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:15 - 10:50am EDTTransition chains of invariant tori around L1 in the Sun-Earth system - Pablo Roldán González, Instituto Tecnológico Autónomo de México (ITAM)11th Floor Lecture Hall
11:00 - 11:35am EDTOn rigorous verification of the crossed mapping condition - Zin Arai, Hokkaido University11th Floor Lecture Hall
11:45 - 12:00pm EDTBreak  
12:00 - 12:35pm EDTOn the bifurcation of hyperbolic invariant manifolds- From Numerics to Rigorous results, and then back to Numerics. - Jordi-Lluís Figueras, Uppsala University11th Floor Lecture Hall
12:45 - 1:00pm EDTGroup Photo in Lecture Hall11th Floor Lecture Hall 
1:00 - 3:00pm EDTBreak for Lunch / Free Time  
3:00 - 5:00pm EDTCollaboration and Work Time  
3:45 - 4:15pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Thursday, April 7, 2016
TimeEventLocationMaterials
9:00 - 9:35am EDTPeriodic solutions for some hyperbolic PDEs - Hans Koch, University of Texas at Austin11th Floor Lecture Hall
9:45 - 10:15am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:15 - 10:50am EDTRigorous estimation of the speed of convergence to equilibrium. - Stefano Galatolo, University of Pisa11th Floor Lecture Hall
11:00 - 11:35am EDTIntroduction to the software package `Dynamics Explorer' for exploration of discrete dynamical systems - Suzanne Lynch Boyd, University of Wisconsin-Milwaukee11th Floor Lecture Hall
11:45 - 12:00pm EDTBreak  
12:00 - 12:35pm EDTSharp mixing rates via inducing w.r.t. general return times - Dalia Terhesiu, University of Vienna11th Floor Lecture Hall
12:45 - 3:00pm EDTBreak for Lunch / Free Time  
3:00 - 3:35pm EDTComputer-assisted proofs for periodic orbits of PDEs - Jean-Philippe Lessard, Université Laval11th Floor Lecture Hall
3:45 - 4:15pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:15 - 4:50pm EDTSet-oriented computation in dynamics - Kathrin Padberg-Gehle, Technische Universität Dresden11th Floor Lecture Hall
Friday, April 8, 2016
TimeEventLocationMaterials
9:00 - 9:35am EDTInterval Analysis Methods for Elliptic Boundary Value Problems - Irina Mitrea, Temple University11th Floor Lecture Hall
9:45 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:05am EDTRigorous Approximation of stationary Measures and Convergence to Equilbrium for Iterated Function Systems - Maurizio Monge, Federal University of Rio de Janeiro (UFRJ)11th Floor Lecture Hall
11:15 - 11:50am EDTSome practical and theoretical issues in computational ergodic theory - Isaia Nisoli, Federal University of Rio de Janeiro (UFRJ)11th Floor Lecture Hall 
12:00 - 12:15pm EDTBreak  
12:15 - 12:50pm EDTMinkowski's question mark function and measure. - Giorgio Mantica, Universita' dell'Insubria11th Floor Lecture Hall 
1:00 - 3:00pm EDTBreak for Lunch / Free Time  
3:00 - 3:35pm EDTMelnikov-type method for splitting of separatrices for an explicit range of small parameter - Piotr Zgliczynski, Jagiellonian University11th Floor Lecture Hall
3:45 - 4:15pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:15 - 4:50pm EDTRigorous integration of dissipative PDEs revisited- chaos in the Kuramoto-Sivashinsky equations. - Daniel Wilczak, Jagiellonian University11th Floor Lecture Hall

Associated Semester Workshops

Dimension and Dynamics
Image for "Dimension and Dynamics"

Lecture Videos

Minkowski's question mark function and measure

Giorgio Mantica
Universita' dell'Insubria
April 8, 2016

Some practical and theoretical issues in computational ergodic theory

Isaia Nisoli
Federal University of Rio de Janeiro (UFRJ)
April 8, 2016

Set-oriented computation in dynamics

Kathrin Padberg-Gehle
Technische Universitat Dresden
April 7, 2016

Periodic solutions for some hyperbolic PDEs

Hans Koch
University of Texas at Austin
April 7, 2016

Conformal maps: Computability and Complexity

Ilia Binder
University of Toronto
April 6, 2016

Transition chains of invariant tori around L1 in the Sun-Earth system

Pablo Roldán González
Instituto Tecnológico Autónomo de México (ITAM)
April 6, 2016

Conley Index Theory, Symbolic Dynamics, and Entropy

Sarah Day
College of William and Mary
April 5, 2016

Dynamic Signatures Generated by Regulatory Networks

Konstantin Mischaikow
Rutgers University
April 5, 2016

Computability and computational complexity in dynamical systems.

Cristóbal Rojas
Universidad Andrés Bello (Santiago)
April 5, 2016

Linear Response- Formulae and Rigorous Approximations

Wael Bahsoun
Loughborough University
April 4, 2016

On the measure of the set of regular parameter values for the quadratic map

Zbigniew Galias
AGH University of Science and Technology
April 4, 2016