# Dynamical Systems Working Seminar

The Dynamical Systems Working Seminar (usually) meets on Wednesdays
from 1:30 to 3:00 p.m. in PHSC 809. For more information about the seminar, contact
Fan Yang
or
Alex Grigo.

## Fall 2020

October 7
1:30 PM (CT) Zoom |
Chris Lutsko
Rutgers | Diffusion in Non-Interacting Particle Systems |

October 28
1:30 PM (CT) Zoom |
Tariq Osman (CANCELLED)
Queen's University at Kingston | Limit Theorems for Quadratic Weyl Sums |

November 4
1:30 PM (CT) Zoom |
Jon Chaika
University of Utah | There exists a weakly mixing billiard in a polygon |

November 11
1:30 PM (CT) Zoom |
Saša Kocić
University of Mississippi | Renormalization, rigidity and universality: from circle maps to Schroedinger operators over them |

December 2
1:30 PM (CT) Zoom |
Kasun Fernando
University of Toronto | Expansions in the mixing local limit theorems for dynamical systems |

## Spring 2020

February 5
1:30 AM (CT) PHSC 809 |
Nikola Petrov
University of Oklahoma | The Poincaré-Siegel theorem - the simplest KAM-type theorem |

February 12
1:30 PM (CT) PHSC 809 |
Nikola Petrov
University of Oklahoma | The Poincaré-Siegel theorem - the simplest KAM-type theorem |

February 19
1:30 PM (CT) PHSC 1105 |
Nikola Petrov
University of Oklahoma | The Poincaré-Siegel theorem - the simplest KAM-type theorem - part II |

February 26
1:30 PM (CT) PHSC 809 |
miro kramar
University of Oklahoma | Conley Index Theory and its Applications |

March 4
1:30 PM (CT) PHSC 809 |
miro kramar
University of Oklahoma | Conley Index Theory and its Applications (Part II) |

March 11
1:30 PM (CT) PHSC 809 |
miro kramar
University of Oklahoma | Conley Index Theory and its Applications (Part III) |

April 15
1:30 PM (CT) Zoom |
Pengfei Zhang
| Elliptic Coordinates and Elliptic Billiards |

Show semesters preceding Fall 2020

## Fall 2019

August 28
2:30 PM (CT) PHSC 1105 |
Nikola Petrov
University of Oklahoma | Hamiltonian dynamics and symplectic geometry - I |

September 4
2:30 PM (CT) PHSC 1105 |
Nikola Petrov
University of Oklahoma | Hamiltonian dynamics and symplectic geometry - II |

September 11
2:30 PM (CT) PHSC 1105 |
Nikola Petrov
University of Oklahoma | Hamiltonian dynamics and symplectic geometry - III |

September 18
2:30 PM (CT) PHSC 1105 |
Jory Griffin
University of Oklahoma | Dynamics on the Hyperbolic Plane - I |

September 25
2:30 PM (CT) PHSC 1105 |
Jory Griffin
University of Oklahoma | Dynamics on the Hyperbolic Plane - II |

October 2
2:30 PM (CT) PHSC 1105 |
Jory Griffin
University of Oklahoma | Dynamics on the Hyperbolic Plane - III |

October 9
2:30 PM (CT) PHSC 1105 |
Fan Yang
University of Oklahoma | A new cross-section for singular flows |

October 16
2:30 PM (CT) PHSC 1105 |
Fan Yang
University of Oklahoma | A new cross-section for singular flows: part 2 |

October 23
2:30 PM (CT) PHSC 1105 |
Fan Yang
University of Oklahoma | A new cross-section for singular flows: part 3 |

November 6
2:30 PM (CT) PHSC 1105 |
Pengfei Zhang
University of Oklahoma | Introduction to Planar Billiards |

November 13
2:30 PM (CT) PHSC 1105 |
Pengfei Zhang
University of Oklahoma | Mechanisms for Chaotic Billiards |

## Spring 2019

January 30
2:30 - 4:00 PM PHSC 1105 |
Alex Grigo
| Deterministic Approximations of Markov Chains |

February 6
2:30 - 4:00 PM PHSC 1105 |
Alex Grigo
University of Oklahoma | Deterministic Approximations of Markov Chains II |

February 13
2:30 - 4:00 PM PHSC 1105 |
Connor Davis
University of Oklahoma | Introduction to Martingales and Some Estimates |

February 20
2:30 - 4:00 PM PHSC 1105 |
Connor Davis
University of Oklahoma | Martingales Continued |

February 27
2:30 - 4:00 PM PHSC 1105 |
Connor Davis
University of Oklahoma | Martingales Continued |

March 6
2:30 - 4:00 PM PHSC 1105 |
Alex Grigo
| Deterministic Approximations of Markov Chains III |

## Fall 2018

September 5
2:30 - 4:00 PM PHSC 1105 |
Alex Grigo
University of Oklahoma | Markov partitions, symbolic coding, entropy |

September 12
2:30 - 4:00 PM PHSC 1105 |
Fan Yang
University of Oklahoma | Unique equilibrium state for Markov shift |

September 19
2:30 - 4:00 PM PHSC 1105 |
Fan Yang
University of Oklahoma | Unique equilibrium state for Markov shift, part 2 |

September 26
2:30 - 4:00 PM PHSC 1105 |
Connor Davis
University of Oklahoma | Dynamical Systems with Hole and Escape Rates |

September 26
2:30 - 4:00 PM PHSC 1105 |
Connor Davis
University of Oklahoma | Dynamical Systems with Hole |

October 10
2:30 - 4:00 PM PHSC 1105 |
Connor Davis
University of Oklahoma | Dynamics With Hole Pt. 2 |

October 24
2:30 - 4:00 PM PHSC 1105 |
Martin Carlson
University of Oklahoma | Product of Expansive Markov Maps with Hole - Part I |

November 7
2:30 - 4:00 PM PHSC 1105 |
Martin Carlson
University of Oklahoma | Product of Expansive Markov Maps with Hole - Part II |

## Spring 2018

March 2
3:30 - 4:30 PM PHSC 809 |
Alex Grigo
University of Oklahoma | Averaging in Hamiltonian systems and other systems |

March 9
3:30 - 4:30 PM PHSC 809 |
Alex Grigo
University of Oklahoma | Averaging - part II |

March 16
3:30 - 4:30 PM PHSC 809 |
Alex Grigo
University of Oklahoma | Averaging - part III |

March 30
3:30 - 4:30 PM PHSC 809 |
Alex Grigo
| Averaging - part iV |

April 6
3:30 - 4:30 PM PHSC 809 |
Mahesh Sunkula
| Hamiltonian systems and Action-Angle coordinates |

April 13
3:30 PM-4:30 PM PHSC 809 |
Mahesh Sunkula
University of Oklahoma | Action-Angle Variables |

## Fall 2017

September 5
10:30 - 11:45 AM PHSC 1105 |
Fan Yang
University of Oklahoma | Decay of correlations for subshift of finite type, part 1 |

September 11
10:30 AM - 11:45 AM PHSC 1105 |
Fan Yang
University of Oklahoma | Decay of correlations for subshift of finite type, part 2 |

September 12
10:30 - 11:45 AM PHSC 1105 |
Fan Yang
University of Oklahoma | Decay of correlations for subshift of finite type, part 2 |

September 19
10:30 - 11:45 AM PHSC 1105 |
Fan Yang
University of Oklahoma | Decay of correlations for subshift of finite type, part 3 |

September 26
10:30 AM - 11:45 AM PHSC 1105 |
Fan Yang
University of Oklahoma | Decay of correlations for subshift of finite type, part 4 |

October 3
10:30 - 11:45 PM PHSC 1105 |
Fan Yang
University of Oklahoma | Decay of correlations for subshift of finite type, part 5 |

October 10
10:30 - 11:45 AM PHSC 1105 |
Fan Yang
University of Oklahoma | Decay of correlations for subshift of finite type, part 6 |

October 17
10:30 - 11:45 AM PHSC 1105 |
Fan Yang
University of Oklahoma | Decay of correlations for subshift of finite type, part 6 |

October 17
10:30 - 11:45 PM PHSC 1105 |
Fan Yang
University of Oklahoma | Decay of correlations for subshift of finite type, part 6 |

October 24
10:30 - 11:45 PM PHSC 1105 |
Alex Grigo
University of Oklahoma | Symbolic coding of smooth systems and Markov Partitions - part 2 |

October 31
10:30 - 11:30 PM PHSC 809 |
Connor Davis
University of Oklahoma | An Interesting Measure Theoretic Example |

November 7
10:30 - 11:45 AM PHSC 1105 |
Pengfei Zhang
University of Oklahoma | Spectral properties of circle maps induced by Blaschke products |

November 14
10:30 - 11:45 PM PHSC 1105 |
Fan Yang
University of Oklahoma | Introduction to Young's tower |

November 21
10:30 AM - 11:45 AM PHSC 1105 |
Fan Yang
University of Oklahoma | Introduction to Young's tower, part 2 |

December 5
10:30 - 11:45 PM PHSC 1105 |
Alex Grigo
| Young towers - examples and comments |

## Spring 2017

February 1
1:00 - 2:15 PM PHSC 1105 |
Alex Grigo
University of Oklahoma | Invariant manifolds |

February 8
1:00 - 2:15 PM PHSC 1105 |
Alex Grigo
University of Oklahoma | Invariant manifolds II |

February 15
1:00 - 2:15 PM PHSC 1105 |
Alex Grigo
University of Oklahoma | Invariant manifolds III |

February 22
1:00 - 2:15 PM PHSC 1105 |
Mahesh Sunkula
University of Oklahoma | Horseshoe map and its invariant set |

March 1
1:00 - 2:15 PM PHSC 1105 |
Mahesh Sunkula
University of Oklahoma | Horseshoe Map Continued.... |

March 22
1:00 - 2:15 PM PHSC 1105 |
Jonathan Epstein
University of Oklahoma | Topological Entropy for Arnold's Cat Map |

## Fall 2016

September 13
3:00 - 4:15 PM PHSC 809 |
Alex Grigo
University of Oklahoma | Introduction to statistical properties of dynamical systems |

September 20
3:00 - 4:15 PM PHSC 809 |
Alex Grigo
University of Oklahoma | Introduction to statistical properties of dynamical systems II |

September 27
3:00 - 4:15 PM PHSC 809 |
Alex Grigo
University of Oklahoma | Introduction to statistical properties of dynamical systems III |

October 11
3:00 - 4:15 PM PHSC 809 |
Mahesh Sunkula
University of Oklahoma | Expanding maps and their spectrum |

October 18
3:00 - 4:15 PM PHSC 809 |
Mahesh Sunkula + Ore Adekoya
University of Oklahoma | Expanding maps and their spectrum II |

October 25
3:00 - 4:15 PM PHSC 809 |
Ore Adekoya + Dania Sheaib
University of Oklahoma | Expanding maps and their spectrum III |

November 8
3:00 - 4:15 PM PHSC 809 |
Dania Sheaib + Connor Davis
University of Oklahoma | General Expanding Maps and Their Spectrum |

November 15
3:00 - 4:00 PM PHSC 809 |
Connor Davis
University of Oklahoma | Introduction to spectral calculus |

November 22
3:00 - 4:15 PM PHSC 809 |
Connor Davis
University of Oklahoma | Introduction to spectral calculus II |

November 29
3:00 - 4:15 PM PHSC 809 |
Alex Grigo
University of Oklahoma | Wrap up of the semester |

## Spring 2016

February 1
4:30 - 5:30 PM PHSC 1105 |
Alex Grigo
University of Oklahoma | Introduction to Levy processes |

February 8
4:30 - 5:30 PM PHSC 1105 |
Alex Grigo
University of Oklahoma | Introduction to Levy processes II |

February 15
4:30 - 5:30 PM PHSC 1105 |
Alex Grigo
University of Oklahoma | Introduction to Levy processes III |

February 22
4:30 - 5:30 PM PHSC 1105 |
Mathew Gluck
University of Oklahoma | Levy Processes and the Fractional Laplacian |

March 7
4:30 - 5:30 PM PHSC 1105 |
Alex Grigo
University of Oklahoma | SDEs driven by Levy processes |

March 28
4:30 - 5:30 PM PHSC 1105 |
Mahesh Sunkula
University of Oklahoma | Stability Conditions and Control of Nonlinear Systems |

April 4
4:30 - 5:30 PM PHSC 1105 |
Mahesh Sunkula
University of Oklahoma | Control of Nonlinear systems |

April 18
4:30-5:30 PM PHSC 1105 |
Nikola Petrov
University of Oklahoma | Poisson and renewal processes - I |

April 25
4:30 - 5:30 PM PHSC 1105 |
Nikola Petrov
University of Oklahoma | Poisson and renewal processes - II |

## Fall 2015

September 8
12:30 - 1:15 PM PHSC 430 |
Alex Grigo
University of Oklahoma | Construction and path regularity of Brownian motion |

September 15
12:00 - 1:15 PM PHSC 430 |
Mahesh Sunkula
University of Oklahoma | Markov and Martingale Properties of Brownian Motion - I |

September 22
12:00 - 1:15 PM PHSC 430 |
Mahesh Sunkula
University of Oklahoma | Markov and Martingale Properties of Brownian Motion - II |

September 29
12:00 - 1:15 PM PHSC 430 |
Mahesh Sunkula
University of Oklahoma | Markov and Martingale Properties of Brownian Motion - III |

October 6
12:00 - 1:15 PM PHSC 430 |
Alex Grigo
University of Oklahoma | Some martingale inequalities and an outlook on stochastic integration |

October 13
12:00 - 1:15 PM PHSC 430 |
Dania Sheaib
University of Oklahoma | Stochastic Integration and Ito's Formula |

October 20
12:00 - 1:15 PM PHSC 430 |
Dania Sheaib
University of Oklahoma | Stochastic Integrals with respect to Brownian Motion |

October 27
12:00 - 1:15 PM PHSC 430 |
Dania Sheaib
University of Oklahoma | Stochastic Integration with respect to Brownian Motion II |

October 28
12:00 - 1:15 PM PHSC 430 |
Dania Sheaib
University of Oklahoma | Stochastic Integration with respect to Brownian Motion II |

November 10
12:00 - 1:15 PM PHSC 430 |
Mahesh Sunkula
University of Oklahoma | Introduction to Stochastic differential equations |

November 17
12:00 - 1:15 PM PHSC 430 |
Mahesh Sunkula
University of Oklahoma | Introduction to Stochastic differential equations -II |

November 24
12:00 - 1:15 PM PHSC 430 |
Alex Grigo
University of Oklahoma | Introduction to stratonovich calculus |

December 1
12:00 - 1:15 PM PHSC 430 |
Dania Sheaib
University of Oklahoma | Euler method for ODEs and SDEs |

December 8
12:00 - 1:15 PM PHSC 430 |
Dania Sheaib
University of Oklahoma | Numerical Solutions to SDE's |

## Spring 2015

January 21
2:30 - 4:00 PM PHSC 1105 |
Nikola Petrov
University of Oklahoma | Geometric approach to first order PDEs - I |

January 28
2:30 - 4:00 PM PHSC 1105 |
Nikola Petrov
University of Oklahoma | Geometric approach to first order PDEs - II |

February 4
2:30 - 4:00 PM PHSC 1105 |
Dania Sheaib
University of Oklahoma | Variational Principle and Hamilton-Jacobi Equations |

February 11
2:30 - 4:00 PM PHSC 1105 |
Dania Shaeib
University of Oklahoma | Variational Principle and Hamilton-Jacobi Equations II |

February 18
2:30 - 4:00 PM PHSC 1105 |
Dania Sheaib
University of Oklahoma | Variational Principle and Hamilton-Jacobi Equations III |

February 25
2:30 - 4:00 PM PHSC 1105 |
Mahesh Sunkula
University of Oklahoma | Symplectic Algebra and Symplectic Manifolds |

March 4
2:30 - 4:00 PM PHSC 1105 |
Mahesh Sunkula
University of Oklahoma | Hamiltonian Systems |

March 11
2:30 - 4:00 PM PHSC 1105 |
Mahesh Sunkula
| Hamiltonian Systems |

March 25
2:30 - 4:00 PM PHSC 1105 |
Mahesh Sunkula
University of Oklahoma | Geometrical Interpretation of Hamilton Jacobi Equation |

April 1
2:30 - 4:00 PM PHSC 1105 |
Garrett Alston
University of Oklahoma | Contact Geometry and Linear PDEs |

April 8
2:30 - 4:00 PM PHSC 1105 |
Garrett Alston
University of Oklahoma | Contact Geometry and First Order PDEs II |

April 22
2:30 - 4:00 PM PHSC 1105 |
Alex Grigo
University of Oklahoma | Introduction to the (mathematical) theory of billiards |

## Fall 2014

September 2
3:00 - 4:00 PM PHSC 809 |
Mahesh Sunkula
University of Oklahoma | Poincare Siegel Theorem - I |

September 9
3:00 - 4:00 PM PHSC 809 |
Mahesh Sunkula
University of Oklahoma | Poincare Siegel Theorem - II |

September 16
3:00 - 4:00 PM PHSC 809 |
Mahesh Sunkula
University of Oklahoma | Poincare Siegel Theorem - III |

September 23
3:00 - 4:00 PM PHSC 809 |
Bryan Archer
University of Oklahoma | A Taste of Normal Forms |

September 30
3:00 - 4:00 PM PHSC 809 |
Bryan Archer
University of Oklahoma | A Taste of Normal Forms II |

October 14
3:00 - 4:00 PM PHSC 809 |
Linling Ru
| Uniformly hyperbolic attractors |

October 21
3:00 - 4:00 PM PHSC 809 |
Linling Ru
| Plykin attractor in discrete time |

October 28
3:00 - 4:00 PM PHSC 809 |
Linling Ru
| Plykin attractor in continuous time |

November 11
3:00 - 4:00 PM PHSC 809 |
Alex Grigo
University of Oklahoma | Hyperbolicity and cones |

## Spring 2014

January 21
3:30 - 4:30 PM PHSC 809 |
Nikola Petrov
University of Oklahoma | An introduction to Hamiltonian dynamics - I |

January 28
3:30 - 4:30 PM PHSC 809 |
Nikola Petrov
University of Oklahoma | An introduction to Hamiltonian dynamics - II |

February 4
3:30 - 4:30 PM PHSC 809 |
James Broda
University of Oklahoma | Geometry for dynamical systems - I |

February 11
3:30 - 4:30 PM PHSC 321 |
James Broda
University of Oklahoma | Geometry for dynamical systems - II |

February 18
3:30 - 4:30 PM PHSC 809 |
James Broda
University of Oklahoma | Geometry for dynamical systems - III |

February 25
3:30 -4:30 PM PHSC 809 |
Bryan Archer
University of Oklahoma | Geometry for dynamical systems - IV |

March 4
3:30 - 4:30 PM PHSC 809 |
Bryan Archer
University of Oklahoma | Geometry for dynamical systems - V |

March 11
3:30 - 4:30 PM PHSC 809 |
Nikola Petrov
University of Oklahoma | Geometry for dynamical systems - VI |

March 25
3:30 - 4:30 PM PHSC 809 |
Nikola Petrov
University of Oklahoma | Geometry for dynamical systems - VII |

April 1
3:30 - 4:30 PM PHSC 809 |
James Broda
University of Oklahoma | Birkhoff normal forms - I |

April 8
3:30 - 4:30 PM PHSC 809 |
James Broda
University of Oklahoma | Birkhoff normal forms - II |

April 15
3:30 - 4:30 PM PHSC 809 |
Alexander Grigo
University of Oklahoma | Variational principles and perturbation theory |

April 22
3:30 - 4:30 PM PHSC 809 |
Alexander Grigo
University of Oklahoma | Variational principles and perturbation theory -- part II |

April 29
3:30 - 4:30 PM PHSC 809 |
Alexander Grigo
University of Oklahoma | Variational principles and perturbation theory -- part III |

## Fall 2013

August 29
10:30 - 11:45 AM PHSC 809 |
Alexander Grigo
University of Oklahoma | ODEs - a crash course, part 1 |

September 5
10:30 - 11:30 AM |
Alexander Grigo
University of Oklahoma | ODEs - a crash course - II |

September 12
10:30 - 11:30 AM PHSC 321 |
Alexander Grigo
University of Oklahoma | ODEs - a crash course - III |

September 19
10:30 - 11:30 AM PHSC 809 |
Mahesh Sunkula
University of Oklahoma | Linearization Methods - I |

September 26
10:30 - 11:30 AM PHSC 809 |
Mahesh Sunkula
University of Oklahoma | Linearization Methods II (For Periodic Orbits) |

October 3
10:30 - 11:30 AM PHSC 809 |
Bryan Archer
University of Oklahoma | A Brief Word On the Duffing and Van der Pol Equations |

October 10
10:30 - 11:30 AM PHSC 809 |
Bryan Archer
University of Oklahoma | A Brief Word On the Duffing and Van der Pol Equations |

October 17
10:30 - 11:30 AM PHSC 809 |
Bryan Archer
University of Oklahoma | A Brief Word On the Duffing and Van der Pol Equations - II |

October 24
10:30 - 11:30 AM PHSC 809 |
James Broda
University of Oklahoma | The WKB method |

October 31
10:30 - 11:45 AM PHSC 809 |
Alex Grigo
University of Oklahoma | Boundary layer techniques |

November 7
10:30 - 11:30 PM PHSC 809 |
Dania Sheaib
University of Oklahoma | Geometric Singular Perturbation in View of Fenichel Theory |

November 21
10:30 - 11:30 AM PHSC 809 |
Dania Sheaib
University of Oklahoma | Geometric Singular Perturbation in View of Fenichel Theory -- part II |

## Spring 2013

March 8
4:30 - 5:30 PM PHSC 321 |
Bryan Archer
University of Oklahoma | The ABC's of circle maps - I |

March 29
4:30 - 5:30 PM PHSC 321 |
Bryan Archer
University of Oklahoma | The ABC's of circle maps - II |

April 5
4:30 - 5:30 PM PHSC 321 |
Bryan Archer
University of Oklahoma | The ABC's of Circle maps - III |

April 12
4:30 - 5:30 PM PHSC 321 |
Nikola Petrov
University of Oklahoma | Periodically pulsating resonators and circle maps - I |

April 19
4:30 - 5:30 PM PHSC 321 |
Nikola Petrov
University of Oklahoma | Periodically pulsating resonators and circle maps - II |