University of Oklahoma   Mathematics Department
Dynamical Systems Working Seminar
Dynamical Systems Working Seminar
This semester, 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.
Spring 2020 Talks
1/27Fan YangOUOrganizational meeting
2/5Nikola PetrovOUThe Poincaré-Siegel theorem - the simplest KAM-type theorem
2/12Nikola PetrovOUThe Poincaré-Siegel theorem - the simplest KAM-type theorem - I
2/19Nikola PetrovOUThe Poincaré-Siegel theorem - the simplest KAM-type theorem - II
2/26Miro KramarOUConley index theory and its applications - I
3/4Miro KramarOUConley index theory and its applications - II
3/11Miro KramarOUConley index theory and its applications - III
4/15Pengfei ZhangOUElliptic coordinates and elliptic billiards
4/22
4/29

Fall 2019 Talks
8/19Fan YangOUOrganizational meeting
8/28Nikola PetrovOUHamiltonian dynamics and symplectic geometry - I
9/4Nikola PetrovOUHamiltonian dynamics and symplectic geometry - II
9/11Nikola PetrovOUHamiltonian dynamics and symplectic geometry - III
9/18Jory GriffinOUDynamics on the hyperbolic plane - I
9/25Jory GriffinOUDynamics on the hyperbolic plane - II
10/2Jory GriffinOUDynamics on the hyperbolic plane - III
10/9Fan YangOUA new cross-section for singular flows - I
10/16Fan YangOUA new cross-section for singular flows - II
10/23Fan YangOUA new cross-section for singular flows - III
11/6Pengfei ZhangOUIntroduction to planar billiards
11/13Pengfei ZhangOUMechanisms for chaotic billiards

Spring 2019 Talks
1/23Organizational meeting
1/30Alex GrigoOUDeterministic approximations of Markov chains - I
2/6Alex GrigoOUDeterministic approximations of Markov chains - II
2/13Connor DavisOUIntroduction to martingales and some estimates
2/20Connor DavisOUMartingales continued
2/27Connor DavisOUMartingales continued
3/6Alex GrigoOUDeterministic approximations of Markov chains - III

Fall 2018 Talks
9/5Alex GrigoOUMarkov partitions, symbolic coding, entropy
9/12Fan YangOUUnique equilibrium state for Markov shift - I
9/19Fan YangOUUnique equilibrium state for Markov shift - II
9/26Connor DavisOUDynamical systems with hole - I
10/3No talk
10/10Connor DavisOUDynamical systems with hole - II
10/17No talk
10/24Martin CarlsonOUProduct of expansive Markov maps with hole - I
10/31No talk
11/7Martin CarlsonOUProduct of expansive Markov maps with hole - II

Spring 2018 Talks
3/2Alex GrigoOUAveraging in Hamiltonian systems and other systems - I
3/9Alex GrigoOUAveraging in Hamiltonian systems and other systems - II
3/16Alex GrigoOUAveraging in Hamiltonian systems and other systems - III
3/30Alex GrigoOUAveraging in Hamiltonian systems and other systems - IV
4/6Mahesh SunkulaOUHamiltonian systems and action-angle coordinates
4/13Mahesh SunkulaOUAction-angle variables

Fall 2017 Talks
8/28, 4 pmOrganizational meeting
9/5Fan YangOUDecay of correlations for subshift of finite type - I
9/12Fan YangOUDecay of correlations for subshift of finite type - II
9/19Fan YangOUDecay of correlations for subshift of finite type - III
9/26Fan YangOUDecay of correlations for subshift of finite type - IV
10/3Fan YangOUDecay of correlations for subshift of finite type - V
10/10Fan YangOUDecay of correlations for subshift of finite type - VI
10/17Alex GrigoOUSymbolic coding of smooth systems and Markov Partitions - I
10/24Alex GrigoOUSymbolic coding of smooth systems and Markov Partitions - II
10/31Connor DavisOUAn interesting measure theoretic example
11/7Pengfei ZhangOUSpectral properties of circle maps induced by Blaschke products
11/14Fan YangOUIntroduction to Young's tower - I
11/21Fan YangOUIntroduction to Young's tower - II
11/28No talk
12/5Alex GrigoOUYoung towers - examples and comments

Spring 2017 Talks
1/25Alex GrigoOUOrganizational meeting
2/1Alex GrigoOUInvariant manifolds - I
2/8Alex GrigoOUInvariant manifolds - II
2/15Alex GrigoOUInvariant manifolds - III
2/22Mahesh SunkulaOUHorseshoe map and its invariant set
3/1Mahesh SunkulaOUHorseshoe map continued
3/8No talk
3/22Jonathan EpsteinOUTopological entropy for Arnold's cat map

Fall 2016 Talks
8/30Organizational meeting
9/13Alex GrigoOUIntroduction to statistical properties of dynamical systems - I
9/20Alex GrigoOUIntroduction to statistical properties of dynamical systems - II
9/27Alex GrigoOUIntroduction to statistical properties of dynamical systems - III
10/4No talk
10/11Mahesh SunkulaOUExpanding maps and their spectrum - I
10/18Mahesh Sunkula, Ore AdekoyaOUExpanding maps and their spectrum - II
10/25Ore Adekoya, Dania SheaibOUExpanding maps and their spectrum - III
11/1No talk
11/8Dania Sheaib, Connor DavisOUGeneral expanding maps and their spectrum
11/15Connor DavisOUIntroduction to spectral calculus - I
11/22Connor DavisIntroduction to spectral calculus - II
11/29Alex GrigoOUWrap up of the semester
12/6No talk

Spring 2016 Talks
1/25Organizational meeting
2/1Alex GrigoOUIntroduction to Levy processes - I
2/8Alex GrigoOUIntroduction to Levy processes - II
2/15Alex GrigoOUIntroduction to Levy processes - III
2/22Mathew GluckOULevy processes and the fractional Laplacian
2/29No talk
3/7Alex GrigoStochastic differential equations driven by Levy processes
3/21No talk
3/28Mahesh SunkulaOUStability conditions and control of nonlinear systems
4/4Mahesh SunkulaOUControl of nonlinear systems
4/11No talk
4/18Nikola PetrovOUPoisson and renewal processes - I
4/25Nikola PetrovOUPoisson and renewal processes - II
5/2 (3:20 pm)Sean BauerOUOn the existence of KAM tori for presymplectic vector fields (Ph.D. thesis defense)

Fall 2015 Talks
9/1Alex GrigoOUOrganizational meeting
9/8Alex GrigoOUConstruction and path regularity of Brownian motion
9/15Mahesh SunkulaOUMarkov and martingale properties of Brownian motion - I
9/22Mahesh SunkulaOUMarkov and martingale properties of Brownian motion - II
9/29Mahesh SunkulaOUMarkov and martingale properties of Brownian motion - III
10/6Alex GrigoOUSome martingale inequalities and an outlook on stochastic integration
10/13Dania SheaibOUStochastic integration and Ito's formula
10/20Dania SheaibOUStochastic integrals with respect to Brownian motion - I
10/27Dania SheaibOUStochastic Integration with respect to Brownian Motion - II
11/3No talk
11/10Mahesh SunkulaOUIntroduction to stochastic differential equations - I
11/17Mahesh SunkulaOUIntroduction to stochastic differential equations - II
11/24Alex GrigoOUIntroduction to Stratonovich calculus
12/1Dania SheaibOUEuler method for ODEs and stochastic differential equations
12/8Dania SheaibOUNumerical solutions to stochastic differential equations

Spring 2015 Talks
1/21Nikola PetrovOUGeometric approach to first order PDEs - I
1/28Nikola PetrovOUGeometric approach to first order PDEs - II
2/4Dania SheaibOUVariational principle and Hamilton-Jacobi equations - I
2/11Dania SheaibOUVariational principle and Hamilton-Jacobi equations - II
2/18Dania SheaibOUVariational principle and Hamilton-Jacobi equations - III
2/25Mahesh SunkulaOUSymplectic algebra and symplectic manifolds
3/4Mahesh SunkulaOUHamiltonian systems
3/11Mahesh SunkulaOUGeometrical interpretation of Hamilton Jacobi equation - I
3/25Mahesh SunkulaOUGeometrical interpretation of Hamilton Jacobi equation - II
4/1Garrett AlstonOUContact geometry and linear PDEs - I
4/8Garrett AlstonOUContact geometry and linear PDEs - II
4/15No talk
4/22Alexander GrigoOUIntroduction to the (mathematical) theory of billiards
4/29 (2-4 pm)Estapraq KahlilOUExistence and stability of solutions to a model equation for dispersion-managed solitary waves (Ph.D. thesis defense)

Fall 2014 Talks
9/2Mahesh SunkulaOUPoincare-Siegel Theorem - I
9/9Mahesh SunkulaOUPoincare-Siegel Theorem - II
9/16Mahesh SunkulaOUPoincare-Siegel Theorem - III
9/23Bryan ArcherOUA taste of normal forms - I
9/30Bryan ArcherOUA taste of normal forms - II
10/7No talk
10/14Linling RuUniformly hyperbolic attractors - I
10/21Linling RuUniformly hyperbolic attractors - II
10/28Linling RuUniformly hyperbolic attractors - III
11/4No talk
11/11Alex GrigoOUHyperbolicity and cones
11/18No talk - Math Day week
11/25No talk
12/2No talk

Spring 2014 Talks
1/21Nikola PetrovOUAn introduction to Hamiltonian dynamics - I
1/28Nikola PetrovOUAn introduction to Hamiltonian dynamics - II
2/4James BrodaOUGeometry for dynamical systems - I
2/11James BrodaOUGeometry for dynamical systems - II
2/18James BrodaOUGeometry for dynamical systems - III
2/25Bryan ArcherOUGeometry for dynamical systems - IV
3/4Bryan ArcherOUGeometry for dynamical systems - V
3/11Nikola PetrovOUGeometry for dynamical systems - VI
3/25Nikola PetrovOUGeometry for dynamical systems - VII
4/1James BrodaOUBirkhoff normal forms - I
4/8James BrodaOUBirkhoff normal forms - II
4/15Alexander GrigoOUVariational principles and perturbation theory - I
4/22Alexander GrigoOUVariational principles and perturbation theory - II
4/29Alexander GrigoOUVariational principles and perturbation theory - III

Fall 2013 Talks
8/29Alexander GrigoOUODEs - a crash course - I
9/5Alexander GrigoOUODEs - a crash course - II
9/12Alexander GrigoOUODEs - a crash course - III
9/19Mahesh SunkulaOULinearization methods - I (for fixed points)
9/26Mahesh SunkulaOULinearization methods - II (for periodic orbits)
10/3Mahesh SunkulaOULinearization methods - III (Floquet theory)
10/10Bryan ArcherOUA brief word on the Duffing and van der Pol equations - I
10/17Bryan ArcherOUA brief word on the Duffing and van der Pol equations - II
10/24James BrodaOUThe WKB method
10/31Alexander GrigoOUBoundary layer techniques
11/7Dania SheaibOUGeometric singular perturbation in view of Fenichel theory - I
11/14OU Math Day - please volunteer!
11/21Dania SheaibOUGeometric singular perturbation in view of Fenichel theory - II
12/5No talk

Spring 2013 Talks
1/25Alexander GrigoOUStatistical properties of dynamical systems - I
2/1Alexander GrigoOUStatistical properties of dynamical systems - II
2/8Alexander GrigoOUStatistical properties of dynamical systems - III
2/15Sean BauerOUMoving from order to chaos - I
2/22Sean BauerOUMoving from order to chaos - II
3/1No talk - AMS Meeting in Oxford
3/8Bryan ArcherOUThe ABC's of circle maps - I
3/15No talk
3/29Bryan ArcherOUThe ABC's of circle maps - II
4/5Bryan ArcherOUThe ABC's of circle maps - III
4/12Nikola PetrovOUPeriodically pulsating resonators and circle maps - I
4/19Nikola PetrovOUPeriodically pulsating resonators and circle maps - II
4/26No talk
5/3No talk

Fall 2012 Talks
8/24Nikola PetrovOULagrangian variational principle and Euler-Lagrange equations
8/31Nikola PetrovOUHamilton's equations
9/7 Alexander GrigoOUMeasurable dynamical systems and introduction to Ergodic Theory - I
9/14Alexander GrigoOUMeasurable dynamical systems and introduction to Ergodic Theory - II
9/21Alexander GrigoOUMeasurable dynamical systems and introduction to Ergodic Theory - III
9/28Sean BauerOUHamiltonian systems and the classical KAM theorem - I
10/5Sean BauerOUHamiltonian systems and the classical KAM theorem - II
10/19Sean BauerOUHamiltonian systems and the classical KAM theorem - III
10/26No talk
11/2James BrodaOUSymplectic geometry and Hamiltonian dynamics - I
11/9James BrodaOUSymplectic geometry and Hamiltonian dynamics - II
11/16James BrodaOUSymplectic geometry and Hamiltonian dynamics - III
11/30No talk
12/7No talk
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