Dynamical Systems Seminar

from Monday
January 01, 2018 to Thursday
May 31, 2018
 Show events for: All Events AGNES Algebraic geometry seminar Algebraic models in geometry seminar Am.Math.Soc. (AMS) Chapter Seminar Analysis Seminar Analysis Seminar Analysis Student Seminar Capsule Research Talks Colloquium Commencement Ceremony Comprehensive Exams Dynamical Systems Seminar Equivalence Method and Exterior Differential Systems Seminar First and Second Year Student Seminar Friday Summer Meeting Geometric Analysis Learning Seminar Geometry/Topology Seminar Grad / Postdoc Professional Development Seminar Graduate Student Seminar Graduate Topology Seminar Grant Proposal Panel Hodge Theory, Moduli and Representation Theory Holiday Party Joint Columbia-CUNY-Stony Brook General Relativity Seminar Math Club Math Day 2016 Math in Jeans Mathematical Writing Seminar Mathematics Education Colloquium Mathematics Summer Camp Mini Course / Dynamics Learning Seminar Mini-School in Geometry Minicourse in Real Enumerative Geometry New Graduate Students NY General Relativity Seminar Postdoc Geometry/Dynamics Seminar Postdoc Seminar RTG Colloquium RTG Seminar RTG Student Geometry Seminar Seminar in Topology and Symplectic Geometry Seminar on algebraic structures in physics Simons Colloquium Simons Lectures Series Singular metrics and direct images Special Algebra / Algebraic Geometry Seminar Special Analysis Seminar Special Colloquium Special Geometry/Topology Seminar Special Lectures Special Seminar in Algebraic Geometry Special Topology Seminar Student Algebraic Geometry Seminar Student Gauge Theory Seminar Student Seminar on Differential Geometry and Analysis Summer Workshop in Topology and Geometry Symplectic Geometry Reading Seminar Symplectic Geometry Seminar Thesis Defense Topology and Symplectic Geometry / Math of Gauge Fields seminar Women in Mathematics Instructions for subscribing to Stony Brook Math Department Calendars

 FridayFebruary 02, 20182:30 PM - 3:30 PM Math Tower P-131 Scott Sutherland, Stony Brook University On the Lebesgue Measure of the Feigenbaum Julia setIn joint work with Artem Dudko (IMPAN), we show that the Julia set of the quadratic Feigenbaum map has Hausdorff dimension less than two and consequently zero Lebesgue measure, answering a long-standing open question. This is established by a combination of new estimation techniques and a rigorous computer-assisted computation.

 FridayFebruary 09, 20182:30 PM - 3:30 PM Math Tower P-131 Dong Chen, Ohio State University KAM-nondegenerate nearly integrable systems with positive metric entropy on arbitrarily small invariant setsIn 1950s Kolmogorov asked the following question, which is closely related to the celebrated KAM theory: Can a non-degenerate nearly integrable Hamiltonian system have a positive Kolmogorov-Sinai entropy (a.k.a. metric entropy)? In this talk we give a positive answer to this question. In fact, examples with positive metric entropy can be constructed by a C^∞ small Lagrangian perturbation of the geodesic flow on any flat Finsler torus. Moreover positive metric entropy is generated in an arbitrarily small tubular neighborhood of any single trajectory. Similar construction applies to general completely integrable Hamiltonian systems as well. This is a joint work with D. Burago and S. Ivanov.

 FridayFebruary 16, 20182:30 PM - 3:30 PM Math Tower P-131 Kei Irie, Kyoto University $C^∞$-closing lemma for three-dimensional Reeb flows via embedded contact homologyI will explain a proof of $C^∞$-closing lemma for three-dimensional Reeb flows and Hamiltonian surface maps, using embedded contact homology (ECH). In particular, the key ingredient of the proof is an asymptotic formula for spectral invariants in ECH, which was proved by Cristofaro-Gardiner, Hutchings, and Ramos. If time permits, I will discuss a conjecture which gives a quantitative refinement of this result.

 FridayFebruary 23, 20182:30 PM - 3:30 PM Math Tower P-131 Zhiqiang Li, Stony Brook University Prime orbit theorems for expanding Thurston mapsAnalogues of the Riemann zeta function were first introduced into geometry by A. Selberg and into dynamics by M. Artin, B. Mazur, and S. Smale. Analytic studies of such dynamical zeta functions yield quantitative information on the distribution of closed geodesics and periodic orbits. We obtain the first Prime Orbit Theorem, as an analogue of the Prime Number Theorem, in complex dynamics outside of hyperbolic maps, for a class of branched covering maps on the $2$-sphere called expanding Thurston maps $f$. More precisely, we show that the number of primitive periodic orbits of $f$, ordered by a weight on each point induced by a non-constant real-valued Hölder continuous function on $S^2$ satisfying some additional regularity conditions, is asymptotically the same as the well-known logarithmic integral, with an exponentially small error term. Such a result follows from our quantitative study of the holomorphic extension properties of the associated dynamical zeta functions and dynamical Dirichlet series. In particular, the above result applies to postcritically-finite rational maps whose Julia set is the whole Riemann sphere. Moreover, we prove that the regularity conditions needed here are generic; and for a Lattès map $f$, a continuously differentiable function satisfies such a condition if and only if it is not cohomologous to a constant. This is a joint work with T. Zheng.

 FridayMarch 02, 20182:30 PM - 3:30 PM Math Tower P-131 Serge Troubetzkoy, Institut de Mathématiques de Marseille TBATBA

 FridayMarch 09, 20182:30 PM - 3:30 PM Math Tower P-131 Vadim Kaimanovich, University of Ottawa TBATBA

 FridayMarch 23, 20182:30 PM - 3:30 PM Math Tower P-131 Juan Rivera-Letelier, University of Rochester TBATBA

 FridayApril 13, 20182:30 PM - 3:30 PM Math Tower P-131 Anand P. Singh, Central University of Rajasthan TBATBA

 FridayApril 20, 20182:30 PM - 3:30 PM Math Tower P-131 Joshua Bowman, Seaver College TBATBA

 FridayApril 27, 20182:30 PM - 3:30 PM Math Tower P-131 Romain Dujardin, Université Pierre et Marie Curie TBATBA

 FridayMay 04, 20182:30 PM - 3:30 PM Math Tower P-131 Leonid Bunimovich, Georgia Tech TBATBA

 Show events for: All Events AGNES Algebraic geometry seminar Algebraic models in geometry seminar Am.Math.Soc. (AMS) Chapter Seminar Analysis Seminar Analysis Seminar Analysis Student Seminar Capsule Research Talks Colloquium Commencement Ceremony Comprehensive Exams Dynamical Systems Seminar Equivalence Method and Exterior Differential Systems Seminar First and Second Year Student Seminar Friday Summer Meeting Geometric Analysis Learning Seminar Geometry/Topology Seminar Grad / Postdoc Professional Development Seminar Graduate Student Seminar Graduate Topology Seminar Grant Proposal Panel Hodge Theory, Moduli and Representation Theory Holiday Party Joint Columbia-CUNY-Stony Brook General Relativity Seminar Math Club Math Day 2016 Math in Jeans Mathematical Writing Seminar Mathematics Education Colloquium Mathematics Summer Camp Mini Course / Dynamics Learning Seminar Mini-School in Geometry Minicourse in Real Enumerative Geometry New Graduate Students NY General Relativity Seminar Postdoc Geometry/Dynamics Seminar Postdoc Seminar RTG Colloquium RTG Seminar RTG Student Geometry Seminar Seminar in Topology and Symplectic Geometry Seminar on algebraic structures in physics Simons Colloquium Simons Lectures Series Singular metrics and direct images Special Algebra / Algebraic Geometry Seminar Special Analysis Seminar Special Colloquium Special Geometry/Topology Seminar Special Lectures Special Seminar in Algebraic Geometry Special Topology Seminar Student Algebraic Geometry Seminar Student Gauge Theory Seminar Student Seminar on Differential Geometry and Analysis Summer Workshop in Topology and Geometry Symplectic Geometry Reading Seminar Symplectic Geometry Seminar Thesis Defense Topology and Symplectic Geometry / Math of Gauge Fields seminar Women in Mathematics Instructions for subscribing to Stony Brook Math Department Calendars