Dynamics Seminar

These seminars are generally on results related to dynamical systems.   This includes ergodic theory, invariant manifold theory, KAM theory, complex dynamics, topological dynamics, and many more.

Results in related fields, e.g. probability theory, theory of computations, statistical mechanics (to name a few), are also welcome.

Previous Dynamics Seminar listings can be found at the following link: http://www.math.toronto.edu/dynamics/

Normally Hyperbolic foliations by circles

by Pablo Carrasco | University of Toronto
Time: 15:00  (Monday, Nov. 22, 2010)
Location: BA6183, Bahen Center, 40 St George St
Abstract:
A continuous flow is said to be periodic (or compact) if all its trajectories are closed. For a periodic flow in a compact manifold a basic question is whether there exist a uniformly upper bound in the periods of the orbits; the existence of this bound ties firmly the geometry of the orbit foliation (meaning, the foliation given by the orbits of the flow) with the transverse structure and allows nice local models for the neighborhoods of the orbits. It was D. Sullivan who in 1976 found an striking counterexample of a periodic flow in the five sphere where there is no upper bound for the periods, and hence preventing the existence of these nice local models. But now suppose that you have a periodic flow on a compact manifold whose orbit foliation $\mathcal{F}$ is normally hyperbolic. Can you say something about the geometry of this foliation, and in particular, is there a uniform upper bound for the periods? In this talk we'll try to answer this and related questions. As a result we will also obtain information about the dynamics of the normally hyperbolic map preserving $\mathcal{F}$.

Dates in this series

· Monday, Feb. 08, 2010: Dynamics of Lagrangian particles beyond the shocks (Konstantin Khanin)
· Monday, Mar. 01, 2010: On the rigidity of circle maps with break singularities (Sasha Kocic)
· Monday, Mar. 08, 2010: Thurston mappings and Galois actions (Sylvain Bonnot)
· Monday, Mar. 15, 2010: Rate of convergence and Kolmogorov Complexity in the Ergodic Theorem (Cristobal Rojas)
· Monday, Mar. 22, 2010: Dynamical charts for irrationally indifferent fixed points (Mitsuhiro Shishikura)
· Monday, Sep. 13, 2010: Thurston equivalence is decidable (joint work with S. Bonnot and M. Braverman) (Michael Yampolsky)
· Monday, Sep. 20, 2010: Decomposition of Thurston maps (Sylvain Bonnot)
· Monday, Sep. 27, 2010: Ergodicity of some open systems with particle-disk interactions (Tanya Yarmola)
· Monday, Oct. 04, 2010: A mechanism for generic Arnold diffusion (Ke Zhang)
· Monday, Oct. 18, 2010: Pentagram map (Fedor Soloviev)
· Monday, Oct. 25, 2010: Semicircular outer billiards (Dimitry Dolgopyat)
· Monday, Nov. 15, 2010: Singular perturbation analysis of the Boltzmann equation (Alexander Grigo)
· Monday, Nov. 22, 2010: Normally Hyperbolic foliations by circles (Pablo Carrasco)
· Monday, Dec. 06, 2010: Rigidity of circle diffeomorphisms with breaks for almost all rotation numbers (Sasa Kocic)
· Monday, Feb. 14, 2011: Subshift factors of the beta-shift are intrinsically ergodic (Dan Thompson)
· Monday, Feb. 28, 2011: Kowalevski-type integrable systems and discriminantly separable polynomials (Vladimir Dragovic)
· Monday, Mar. 07, 2011: Exponentially small splitting of separatrices for one and a half degrees of freedom Hamiltonian Systems close to a resonance (Marcel Guardia)
· Monday, Mar. 28, 2011: Existence and non-existence of KAM tori near an invariant torus of a Hamiltonian system with Diophantine frequency (Bassam Fayad)
· Monday, Sep. 19, 2011: Multi-dimensional Fatou bifurcation (Igor Gorbovickis)
· Wednesday, Sep. 28, 2011: KAM theory for dissipative systems (Renato Calleja)
· Monday, Oct. 03, 2011: Hyperbolicity of the minimizer for some randomly kicked Hamiltonian systems (Ke Zhang)
· Monday, Oct. 31, 2011: Thermodynamics with small obstructions (Vaughn Climenhaga)
· Monday, Nov. 07, 2011: The Consequences of Quasi-Isometry (Andy Hammerlindl)
· Monday, Nov. 14, 2011: Global well-posedness of a barely supercritical surface quasi-geostrophic equation (Michael Dabkowski)
· Wednesday, Nov. 23, 2011: A proof of Pilgrim's conjecture (Nikita Selinger)
· Friday, Nov. 25, 2011: Critical Locus for Complex Hénon Maps (Tanya Firsova)
· Monday, Jan. 16, 2012: Convergence of renormalizations and rigidity theory for circle diffeomorphisms with a break (Sasa Kocic)
· Monday, Sep. 17, 2012: Perturbing Misiurewicz parameters in the exponential family (Neil Dobbs)
· Monday, Oct. 01, 2012: Homogenization of convex Hamiltonians on arbitrary manifolds (Renato Iturriaga)
· Wednesday, Oct. 24, 2012: Computability and computational complexity of Julia sets (Michael Yampolsky)
· Friday, Oct. 26, 2012: Limit theorems for toral translations (Dmitry Dolgopyat)
· Monday, Oct. 29, 2012: A method to estimate the Lyapunov exponents for some quasi-periodic Schr\"{o}dinger cocycles (Kristian Bjerklov)
· Monday, Jan. 14, 2013: Renormalization and rigidity theory for circle diffeomorphisms with breaks (Sasha Kocic)
· Monday, Jan. 21, 2013: Dynamics of parabolic germs via Resurgence Theory (Artem Dudko)
· Monday, Feb. 04, 2013: Renormalization for Lorenz maps (Denis Gaydashev)