Home /  Introductory Workshop on Dynamical Systems with Emphasis on Extended Systems


Introductory Workshop on Dynamical Systems with Emphasis on Extended Systems January 22, 2007 - January 26, 2007
Registration Deadline: January 08, 2007 over 17 years ago
To apply for Funding you must register by: October 22, 2006 over 17 years ago
Parent Program:
Organizers Chris Jones (U North Carolina), Edgar Knobloch (UC-Berkeley-Physics), Nancy Kopell (Boston U), Lai-Sang Young (chair, Courant)

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The aim of this workshop is to promote the interaction of researchers working on pure and applied aspects dynamical systems. It will feature a group of speakers from mathematics who are responsible for some of the ma advances in the theory of dynamical systems over recent years. They will be complemented with speakers working ispecific applied areas where dynamical systems ideas are used, such as neuroscience, atmospheric sciences, fluidschemical reactions. We plan to have overview talks the aim of which is for each of these groups to introduce thework and techniques to the other, and more specialized talks that center on specific recent advances. Schedule MONDAY, January 22 Welcome 9:15 AM -10:00 AM Smale, Steve: “Dynamics of emergence and flocking” 10:30 AM -11:15 AM Golubitsky, Martin: “Bifurcations in Coupled Systems” 11:15 AM -12:00 PM Kaloshin, Vadim: “Oscillatory motions, Arnold diffusion, and nonlocal instabilities for the planar 3 body problem” 12:00 PM – 1:30 PM LUNCH 1:30 PM - 2:30 PM Mather, John: “Aspects of Arnold Diffusion” 3:00 PM - 3:45 PM Levi, Mark: “Simple examples of Arnold diffusion” TUESDAY, January 23 9:00 AM - 9:45 AM Pesin, Yakov: “Genericity of chaotic dynamics” 9:45 AM -10:30 AM Bunimovich, Leonid: “Dynamical Networks” 11:00 AM -12:00 PM Young, Lai-Sang: “Rank one attractors and weak chaos” 12:00 PM – 2:00 PM LUNCH 2:00 PM - 3:00 PM Chernov, Nikolai: “Chaotic billiards” 3:30 PM - 4:15 PM Dolgopyat, Dmitry: "Recurrence properties of finite horizon Galton board" 4:15 PM - 5:00 PM Pikovsky, Arkady: “Autonomous coupled oscillators with hyperbolic strange attractors” 5:00 PM – 6:00 PM Welcome Reception WEDNESDAY, January 24 9:00 AM - 9:45 AM Evans, Craig : “PDE methods for weak KAM theory” 9:45 AM -10:30 AM Mischaikow, Konstantin: “Computational Dynamics and Homology” 11:00 AM -12:00 PM Doelman, Arjen: “Dynamics of reaction-diffusion patterns” 12:00 PM – 2:00 PM LUNCH 2:00 PM - 3:00 PM Sandstede, Bjorn: “Dynamics of nonlinear waves” 3:30 PM - 4:15 PM Titi, Edriss: “Dynamical Systems Approach to Turbulence” 4:30 PM - 6:30 PM Short Presentations THURSDAY, January 25 9:00 AM - 9:45 AM Zaslavsky, George: “Pseudochaos” 9:45 AM -10:30 AM Hunt, Brian: “Efficient Data Assimilation for Spatially Extended Systems” 11:00 AM -12:00 PM Jones, Christopher: “Do Invariant Manifolds Hold water?” 12:00 PM – 1:45 PM LUNCH 1:45 PM - 2:30 PM Marsden, Jerrold: “Lagrangian coherent structures” 2:30 PM - 3:15 PM Terman, David: “Reducing Neuronal Systems to Discrete Dynamics” UC Colloquium FRIDAY, January 26 9:00 AM - 9:45 AM Guckenheimer, John: “Bifurcations of Relaxation Oscillations” 9:45 AM -10:30 AM Lin, Kevin: “Reliable and Unreliable Behavior in Coupled Oscillator Networks” 11:00 AM -12:00 PM Kopell, Nancy: “Rhythmic dynamics of the nervous system” 12:00 PM – 1:30 PM LUNCH 1:30 PM - 2:15 PM Borisyuk, Alla: “The dynamic range of bursting in a network of respiratory pacemaker cells” 2:15 PM - 3:00 PM Holmes, Philip: “A central pattern generator for insect locomotion: Phase response curves, averaging and reduction ionic current models of bursting neurons” Short presentations by postdocs Wednesday, January 24, 4:30-6:30 Jorge deFreitas, University of Porto: Statistical stability for Hénon maps of the Benedicks-Carleson type Joyce Macabea, UC-Berkeley and MSRI: Quantifying and analyzing the pheromone response system for mating in yeast Mason Porter, Caltech: Nonlinearity Management in Optics Maria Leite, Purdue University: Coupled Systems of ODE's and Their Coupling Structure Nikola Popovic, Boston University: Mixed-mode oscillations and the canard phenomenon: an example Amit Apte, UNC-CH and MSRI: A Bayesian approach to data assimilation Aaron Hoffman, Boston University: Lattice Differential Equations Zoi Rapti, University of Illinois, Urbana-Champaign: Counting eigenvalues via the Evans function Abdul Kane, University of Toronto: Spatio-temporal patterns of activity in large scale neuronal networks Alice Jukes, Imperial College: Homoclinic bifurcation with symmetry Claire Postlethwaite, Northwestern University: Feedback control of patterns Vahagn Manukian, North Carolina State University: Traveling Waves of Surfactant Equations Emily Burkhead, Santa Fe Institute: A dynamical systems approach to the study of cellular automata Margaret Beck, University of Surrey and MSRI: Stability of solutions to PDEs Hamzi Boumediene, UC Davis and MSRI: Elements of the Dynamical Theory of Control Dan Wiley, Howard University and MSRI: Nonlocally Coupled Phase Oscillators Mark Demers, Fairfield University and MSRI: Stability of Statistical Properties via Lasota-Yorke Inequalities Anna Ghazaryan, University of North Carolina: Traveling Waves in Porous Media Combustion: Uniqueness of Waves of Small Thermal Diffusivity
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Funding & Logistics Show All Collapse

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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent PhDs, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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For information about recommended hotels for visits of under 30 days, visit Short-Term Housing. Questions? Contact coord@slmath.org.

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Schedule, Notes/Handouts & Videos
Show Schedule, Notes/Handouts & Videos
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Jan 22, 2007
09:15 AM - 10:00 AM
  Dynamics of Emergence and Flocking.
Steve Smale (University of California, Berkeley)
10:30 AM - 11:15 AM
  Bifurcations in Coupled Systems
Martin Golubitsky
11:15 AM - 12:00 PM
  Oscillatory Motions. Arnold Diffusion, and Nonlocal Instabilities for the Planer 3 Body Problem
vadim kaloshin (University of Maryland)
01:30 PM - 02:30 PM
  Aspects of Arnold Diffusion
John Mather
03:00 PM - 03:45 PM
  Simple Examples of Arnold Diffusion
Mark Levi
Jan 23, 2007
09:00 AM - 09:45 AM
  Genericity of Chaotic Dynamics
Yakov Pesin (Pennsylvania State University)
09:45 AM - 10:30 AM
  Dynamical Networks
Leonid Bunimovich (Georgia Institute of Technology)
11:00 AM - 12:00 PM
  Rank One Attractors and Weak Chaos
Lai-Sang Young (New York University, Courant Institute)
02:00 PM - 03:00 PM
  Chaotic billiards
Nikolai Chernov
03:30 PM - 04:15 PM
  Recurrence Properties of Finite Horizon Galton Board
Dmitry Dolgopyat
04:15 PM - 05:00 PM
  Autonomous Coupled Oscillators with Hyperbolic Strange Attractors
Arkady Pikovsky
Jan 24, 2007
09:00 AM - 09:45 AM
  PDE Methods for Weak KAM Theory
Lawrence Evans (University of California, Berkeley)
09:45 AM - 10:30 AM
  Computational Dynamics and Homology
Konstantin Mischaikow (Rutgers University)
11:00 AM - 12:00 PM
  Dynamics of Reaction-Diffusion Patterns
Arjen Doelman
02:00 PM - 03:00 PM
  Dynamics of Nonlinear Waves
Bjorn Sandstede
03:30 PM - 04:15 PM
  Dynamical Systems Approach to Turbulence
Edriss Titi
Jan 25, 2007
09:00 AM - 09:45 AM
George Zaslavsky
09:45 AM - 10:30 AM
  Efficient Data Assimilation for Spatially Extended Systems
Brian Hunt
11:00 AM - 12:00 PM
  Do Invariant Manifolds Hold Water
Christopher Jones (Brown University)
01:45 PM - 02:30 PM
  Lagrangian Coherent Structures
Jerrold Marsden
02:30 PM - 03:15 PM
  Dynamics of 3D Volume-Preserving Maps
James Meiss (University of Colorado at Boulder)
Jan 26, 2007
09:00 AM - 09:45 AM
  Reducing Neuronal Systems to Discrete Dynamics
David Terman
09:45 AM - 10:30 AM
  Reliable and Unreliable Behavior in Coupled Oscillator Networks
Kevin Lin (University of Arizona)
11:00 AM - 12:00 PM
  Rhythmic Dynamics of the Nervous System
Nancy Kopell (Boston University)
01:30 PM - 02:15 PM
  The dynamic range of bursting in a network of respiratory pacemaker cells
Alla Borisyuk
02:15 PM - 03:00 PM
  A Central Pattern Generator for Insect Locomotion: Phase Response Curves, Averaging and Reduction Ionic Current Models of Bursting Neurons
Philip Holmes (Princeton University)