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Cohomology in algebra, geometry, physicsand statistics
First lecture: Local entropy for finite time dynamics, Second lecture: On the behavior of the Diaconis-Freedman chain in a multi-dimensional simplex
Speaker’s name:
Hoang Duc Luu and Tat Dat Tran
Speaker’s affiliation:
MPI MIS Leipzig
Place:
in IM building, ground floor
Date:
Wednesday, 22. May 2019 - 11:15 to 12:45
Abstract:
Local entropy for finite time dynamics (by Hoang Duc Luu)
Abstract: This talk aims to introduce a concept of entropy for difference and differential equations which is a local-in-space and transient-in-time version of the classical concept of metric entropy. Based on that, a finite-time version of Pesin’s entropy formula arederived. I would also discuss about how to apply the finite-time entropy field to detect special dynamical behavior such as Lagrangian coherent structures, and how to relate the topic to information geometry.
On the behavior of the Diaconis-Freedman chain in a multi-dimensional simplex (by Tat Dat Tran)
Abstract: In this talk, I consider the asymptotic behavior of a Diaconis-Freedman chain in a multi-dimensional simplex from the point of view of the iterated function systems. I first give out some sufficient conditions to have a unique invariant probability measure. I then give out explicit formulas of invariant probability density in some special cases. Finally, I illustrate a completely classify of all behaviors of this chain in two dimensional. This is the joint work with Juergen Jost and Marc Peigne.
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The seminar starts at 11.15 today, since we have two lectures!
Abstract: This talk aims to introduce a concept of entropy for difference and differential equations which is a local-in-space and transient-in-time version of the classical concept of metric entropy. Based on that, a finite-time version of Pesin’s entropy formula arederived. I would also discuss about how to apply the finite-time entropy field to detect special dynamical behavior such as Lagrangian coherent structures, and how to relate the topic to information geometry.
On the behavior of the Diaconis-Freedman chain in a multi-dimensional simplex (by Tat Dat Tran)
Abstract: In this talk, I consider the asymptotic behavior of a Diaconis-Freedman chain in a multi-dimensional simplex from the point of view of the iterated function systems. I first give out some sufficient conditions to have a unique invariant probability measure. I then give out explicit formulas of invariant probability density in some special cases. Finally, I illustrate a completely classify of all behaviors of this chain in two dimensional. This is the joint work with Juergen Jost and Marc Peigne.
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The seminar starts at 11.15 today, since we have two lectures!