| Data/Date | Prelegent/Speaker | Temat/Topic |
|---|---|---|
| 11.01.2024 | Marek Kryspin | Oseledets Decomposition on Sub semiflows - part 2 |
| Abstract: The topic of Oseledets decomposition will be discussed, in particular the conditions under which it is possible to transfer the Oseledets splitting of a Banach space into continuously embedded subspaces of the former. The subject matter is a natural issue related to the phase space (initial conditions space) decomposition in differential equations with or without delay. Such a decomposition provides a complete characterisation of the Lyapunov exponents that govern the dynamics of the system. |
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| Data/Date | Prelegent/Speaker | Temat/Topic |
|---|---|---|
| 11.01.2024 | Marek Kryspin | Oseledets Decomposition on Sub semiflows |
| Abstract: The topic of Oseledets decomposition will be discussed, in particular the conditions under which it is possible to transfer the Oseledets splitting of a Banach space into continuously embedded subspaces of the former. The subject matter is a natural issue related to the phase space (initial conditions space) decomposition in differential equations with or without delay. Such a decomposition provides a complete characterisation of the Lyapunov exponents that govern the dynamics of the system. |
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| 14.12.2023 | Sebastian Kopacz | Uniquely ergodic quasitilings of amenable groups - pt. 4 |
| Abstract |
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| 30.11.2023 | Sebastian Kopacz | Uniquely ergodic quasitilings of amenable groups - pt. 3 |
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Abstract Recording |
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| 23.11.2023 | Sebastian Kopacz | Uniquely ergodic quasitilings of amenable groups - pt. 2 |
|
Abstract Recording |
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| 16.11.2023 | Sebastian Kopacz | Uniquely ergodic quasitilings of amenable groups |
| Abstract:
For a countable amenable group $G$ we prove the existence of a uniquely ergodic, zero entropy quasitiling of $G$,
whose tiles have arbitrarily good invariance properties. This improves the quasitiling construction of Downarowicz, Huczek and Zhang
by adding unique ergodicity.
Recording
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| 19.10.2023 (room A.1.14, building C-19) |
Tomasz Downarowicz | Topological normality preservation by addition |
| Abstract:
In this lecture, inaugural for the seminar in the academic year 2023/2024, I will present something perhaps interesting, very
natural and - above all - easy to follow, namely, a surprising answer
to the question given below:
A symbolic sequence $x$ over a finite alphabet $A= \{0,1,2,...,r-1\}$ is called topologically normal if it is transitive in the full shift over A. In the shift space we introduce coordinatewise addition modulo $r$. What sequences $y$ over $A$ have the property that $x + y$ is topologically normal for every topologically normal sequence $x$? The answer is surprising, because it involves a new class of sequences that presumably none of us has ever heard about before. |
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