## 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/

### A proof of Pilgrim's conjecture

by Nikita Selinger | Stony Brook University
Time: 11:00  (Wednesday, Nov. 23, 2011)
Location: BA2135, Bahen Center, 40 St. George St.
Abstract:
Let $f$ be a postcritically finite branched self-cover of a 2-dimensional topological sphere. Such a map induces an analytic self-map $\sigma_f$ of a finite-dimensional Teichm\"uller space. We prove that this map extends continuously to the augmented Teichm\"uller space and give an explicit construction for this extension. This allows us to characterize the dynamics of Thurston's pullback map near invariant strata of the boundary of the augmented Teichm\"uller space. The resulting classification of invariant boundary strata is used to prove a conjecture by Pilgrim.

#### 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)