### Student Dynamics Archives for Academic Year 2015

#### Organization meeting

When: Tue, September 1, 2015 - 3:30pm

Where: MATH 1310

Speaker: () -

#### Mautner phenomenon

When: Tue, September 8, 2015 - 3:30pm

Where: MATH 1310

Speaker: Minsung Kim (UMD) -

Abstract: Mautner phenomenon gives invariance of unitary representation of simple Lie group. The talk will focus on the case of SL(2,R) and introduction to G-space.

#### Preservation of Periodicity in Variational Integrators

When: Tue, September 15, 2015 - 3:30pm

Where: MATH 1310

Speaker: Jianlong Liu (UMD) -

Abstract: Classical numerical integrators do not preserve symplecticity, a structure inherent in Hamiltonian systems. Thus, the trajectories they produce cannot be expected to possess the same qualitative behavior observed in the original system. Pooling recent results from O'Neale and West, we explore a particular class of numerical integrators, the variational integrator, that preserves one aspect of the range of behavior present in Hamiltonian systems, the periodicity of trajectories.

#### Invariant cones : a means of studying chaotic systems

When: Tue, September 22, 2015 - 3:30pm

Where: MATH 1310

Speaker: Suddhasattwa Das (UMD) -

Abstract: Chaotic systems are characterized by sensitive dependence on initial conditions, dense trajectories and dense periodic points. Due to their occurrence in a wide variety of dynamical systems, they can usually be rigorously studied only if accompanied by some assumptions on the geometric / differential properties of the transformation. One geometric structure which is well understood is the class of Anosov diffeomorphisms or more generally, completely hyperbolic systems and to some extent, partially hyperbolic systems. A weaker version of these rather stringent assumptions is the concept of invariant cones. This is an invariant structure in the tangent bundle of a map and we will explore various consequences of this invariant structure. We will mostly focus on a broad class of maps on the torus and derive various properties and also discuss the interplay between them, under the assumption that a "dominated invariant cone system" is present.

#### The Multiplicative Ergodic Theorem

When: Tue, September 29, 2015 - 3:30pm

Where: Math 1310

Speaker: Hamid Al-Saqban (UMD) -

#### The Horocycle Flow and Some of Its Properties

When: Tue, October 6, 2015 - 3:30pm

Where: MATH 1310

Speaker: Simonelli, Lucia Dora (UMD) -

#### Homoclonic tangency and infinitely many sinks

When: Tue, October 13, 2015 - 3:30pm

Where: MATH 1310

Speaker: Jing Zhou (UMD) -

#### Ergodicity of group action

When: Tue, November 17, 2015 - 3:30pm

Where: MATH 1310

Speaker: Akurugodage, B. Kasun Fernando (UMD) -

#### Quasicrystals and the Dynamics of tiling spaces: part 1

When: Tue, November 24, 2015 - 3:30pm

Where: MATH 1310

Speaker: Schmieding, Scott (UMD) -

#### Quasicrystals and the Dynamics of tiling spaces: part 2

When: Tue, December 1, 2015 - 3:30pm

Where: MATH 1310

Speaker: Schmieding, Scott Edward (UMD) -

#### Ergodic theory and Effective Equidistribution

When: Tue, December 8, 2015 - 3:30pm

Where: MATH 1310

Speaker: Minsung Kim (UMD) -

#### Organization meeting

When: Tue, February 2, 2016 - 3:30pm

Where: MATH 1310

Speaker: () -

#### Invariant distributions and Cohomological Equation

When: Tue, February 9, 2016 - 3:30pm

Where: MATH 1310

Speaker: Minsung Kim (UMD) -

#### Equidistribution of spheres and the orbit counting problem

When: Tue, February 16, 2016 - 3:30pm

Where: Math 1310

Speaker: Hamid Al-Saqban (UMD) - http://math.umd.edu/~hqs

#### Rohlin towers and Statistics of return times

When: Tue, March 1, 2016 - 3:30pm

Where: MATH 1310

Speaker: Suddhasattwa Das (UMD) -

#### Transfer operator and SRB measure for Smooth expanding maps on manifolds

When: Thu, March 24, 2016 - 3:30pm

Where: MATH 1310

Speaker: Jing Zhou (UMD) -

#### Transfer operator and SRB measure for smooth expanding maps (Part II) - CLT and Stochastic Stability.

When: Tue, April 5, 2016 - 3:30pm

Where: MATH 1310

Speaker: Akurugodage, B. Kasun Fernando (UMD) -