RIT on Hamiltonian Dynamics Archives for Fall 2023 to Spring 2024

---

Panarama of Hamiltonian Dynamics

When: Tue, October 4, 2022 - 3:00pm
Where: Kirwan Hall 1308
Speaker: Bassam Fayad (UMD) -
Abstract: We describe the main directions of research in Hamiltonian dynamics and present a selections of open problems

---

KAM tutorial

When: Tue, October 11, 2022 - 3:00pm
Where: Kirwan Hall 1308
Speaker: Bassam Fayad (UMD) -

---

variational approach to second species solutions

When: Tue, October 18, 2022 - 3:00pm
Where: Kirwan Hall 1308
Speaker: Vaughn Osterman (UMD) -

---

Properly Degenerate KAM theory

When: Tue, October 25, 2022 - 3:00am
Where: Kirwan Hall 1308
Speaker: Jaime Paradela (University of Barcelona) -

---

Bolzmann Grad limit for integrable systems

When: Fri, December 2, 2022 - 11:00am
Where: Kirwan Hall 3206
Speaker: Dmitry Dolgopyat (UMD) - https://www.math.umd.edu/~dolgop/

---

Boltzmann Grad limit for integrable systems-2

When: Tue, December 6, 2022 - 3:00pm
Where: Kirwan Hall 1308
Speaker: Dmitry Dolgopyta (UMD) - https://www.math.umd.edu/~dolgop/

---

KAM theory for the nonlinear Schrodinger equation

When: Tue, December 13, 2022 - 1:30pm
Where: MATH0104
Speaker: Jaime Paradela (Barcelona) -

---

Local rigidity of commuting affine automorphisms of the torus

When: Tue, February 7, 2023 - 3:00am
Where: Kirwan Hall 1308
Speaker: Bassam Fayad (UMD) -

---

Local rigidity of commuting affine automorphisms of the torus-2

When: Tue, March 14, 2023 - 3:00pm
Where: Kirwan Hall 1308
Speaker: Bassam Fayad (UMD) -
Abstract: We explore the role of the hyperbolic and parabolic higher rank trick in the local rigidity theory of abelian affine actions on the torus.

---

Anosov averaging theorem

When: Tue, March 28, 2023 - 3:00pm
Where: Kirwan Hall 1308
Speaker: Dmitry Dolgopyat (UMD) -
Abstract: We justify the averaging principle for slow fast systems in the case where the frozen
motion is ergodic on almost every level set. We then discuss the rate of convergence in
the important case where the fast motion is quasiperiodic

---

Near-Collision Orbits in the Planar Circular Restricted 3-Body Problem

When: Tue, April 4, 2023 - 3:00pm
Where: Kirwan Hall 1308
Speaker: Vaughn Osterman (UMD) -
Abstract: We consider orbits in the planar circular restricted 3-body problem containing repeated near-collisions with the smaller primary. A theorem of Font, Nunes, and Simó states that there exists such an orbit shadowing any sequence of collision orbits satisfying certain conditions. This is proven by estimating the Poincaré map from one near-collision to the next and showing that it is a horseshoe map. It follows that there is an invariant hyperbolic set on which this map is conjugated to a subshift on an alphabet of collision orbits.

---

Beyond analytic cicrcles diffeomorphisms and rotations rigidity

When: Tue, April 11, 2023 - 3:00pm
Where: Kirwan Hall 1308
Speaker: Laurent Stolovitch (Université Côte d'Azur) - https://math.unice.fr/~stolo/

---

Spectral Rigidity of convex planar billiards

When: Mon, April 17, 2023 - 10:00am
Where: Kirwan Hall 3206
Speaker: Vadim Kaloshin (IST (Austria)) - https://ist.ac.at/en/research/kaloshin-group/
Abstract: Motivated by the question of M. Kac: Can you hear the shape of a drum?
We introduce the Laplace spectrum and the length spectrum for convex planar domains. After showing a connection between the two spectra we shall discuss
problems of spectral rigidity, namely, if it is possible to smoothly deform a domain
without changing its spectra.

---

Newhouse phenomenon in the complex Hénon family

When: Tue, May 16, 2023 - 3:00pm
Where: Kirwan Hall 1308
Speaker: Zhiyuan Zhang (Paris 13) -
Abstract: In a work in progress with Artur Avila and Mikhail Lyubich, we
show that there are maps in the complex Hénon family with a stable
homoclinic tangency. We will first review Newhouse’s phenomenon for
real surface dynamics and related results. Then we explain how this
phenomenon is related to stable intersections between Cantor sets. Then
we will explain a new mechanism on the stable intersections between two
dynamical Cantor sets generated by two classes of conformal IFSs on the
complex plane.

---