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Vorlesung: 03-M-SP-13 Ergodic Theory - Details

Vorlesung: 03-M-SP-13 Ergodic Theory - Details

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Veranstaltungsname Vorlesung: 03-M-SP-13 Ergodic Theory
Untertitel
Veranstaltungsnummer 03-M-SP-13
Semester SoSe 2025
Aktuelle Anzahl der Teilnehmenden 20
erwartete Teilnehmendenanzahl 20
Heimat-Einrichtung Mathematik
Veranstaltungstyp Vorlesung in der Kategorie Lehre
Erster Termin Montag, 07.04.2025 10:00 - 12:00, Ort: MZH 4140
Art/Form
Englischsprachige Veranstaltung Ja
ECTS-Punkte 9

Räume und Zeiten

MZH 4140
Montag: 10:00 - 12:00, wöchentlich (12x)
Dienstag: 10:00 - 12:00, wöchentlich (14x)
Mittwoch: 16:00 - 18:00, wöchentlich (14x)
Freitag: 08:00 - 10:00, wöchentlich (13x)

Modulzuordnungen

Kommentar/Beschreibung

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!