In the mathematics of dynamical systems, the concept of Lyapunov dimension was suggested by Kaplan and Yorke for estimating the Hausdorff dimension of attractors. Further the concept has been developed and rigorously justified in a number of papers, and nowadays various different approaches to the definition of Lyapunov dimension are used. Remark that the attractors with noninteger Hausdorff dimension are called strange attractors. Since the direct numerical computation of the Hausdorff dimension of attractors is often a problem of high numerical complexity, estimations via the Lyapunov dimension became widely spread.The Lyapunov dimension was named after the Russian mathematician Aleksandr Lyapunov because of the close connection with the Lyapunov exponents. (Wikipedia).
From playlist Dimensions Russian / Pусский
From playlist Dimensions Russian / Pусский
Chapter 2 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Chapter 1 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
From playlist Dimensions Arabe/Arabic / العربية
Chapter 5 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Dimensions (1 of 3: The Traditional Definition - Directions)
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From playlist Exploring Mathematics: Fractals
Concentration inequalities for linear cocycles and their applications to problems...- Silvius Klein
Analysis Seminar Topic: Concentration inequalities for linear cocycles and their applications to problems in dynamics and mathematical physics Speaker: Silvius Klein Affiliation: Pontifical Catholic University of Rio de Janeiro (PUC-Rio), Brazil Date: January 31, 2018 For more videos, pl
From playlist Mathematics
Machine learning analysis of chaos and vice versa - Edward Ott, University of Maryland
About the talk In this talk we first consider the situation where one is interested in gaining understanding of general dynamical properties of a chaotically time evolving system solely through access to time series measurements that depend on the evolving state of an, otherwise unknown,
From playlist Turing Seminars
Weak Hyperbolicity for Singular Flows by Luciana Silva Salgado
PROGRAM SMOOTH AND HOMOGENEOUS DYNAMICS ORGANIZERS: Anish Ghosh, Stefano Luzzatto and Marcelo Viana DATE: 23 September 2019 to 04 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases.
From playlist Smooth And Homogeneous Dynamics
Lyapunov exponents, from the 1960's to the 2020's by Marcelo Viana
DISTINGUISHED LECTURES LYAPUNOV EXPONENTS, FROM THE 1960'S TO THE 2020'S SPEAKER: Marcelo Viana (IMPA, Brazil) DATE: 24 September 2019, 16:00 to 17:30 VENUE: Ramanujan Lecture Hall The ergodic theory of Lyapunov exponents, initiated by the work of Furstenberg and Kesten at the dawn of
From playlist DISTINGUISHED LECTURES
Chapter 6 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
C. Favre - Degeneration of measures of maximal entropy
Consider any meromorphic family of endomorphisms of the complex projective plane parameterized by the punctured unit disk. We shall explain how to describe the behaviour of their measures of maximal entropy when one approaches the central fiber. This generalizes works by Demarco and Fab
From playlist Complex analytic and differential geometry - a conference in honor of Jean-Pierre Demailly - 6-9 juin 2017
From playlist Dimensions Arabe/Arabic / العربية
Local quenches and quantum chaos from higher spin perturbations by Surbhi Khetrapal
Bangalore Area Strings Meeting - 2017 TIME : 31 July 2017 to 02 August 2017 VENUE:Madhava Lecture Hall, ICTS Bangalore Bengaluru now has a large group of string theorists, with 9 faculty members in the area, between ICTS and IISc. This is apart from a large group of postdocs and graduate
From playlist Bangalore Area Strings Meeting - 2017
Lyapunov Stability via Sperner's Lemma
We go on whistle stop tour of one of the most fundamental tools from control theory: the Lyapunov function. But with a twist from combinatorics and topology. For more on Sperner's Lemma, including a simple derivation, please see the following wonderful video, which was my main source of i
From playlist Summer of Math Exposition Youtube Videos
A Toy Model for Time Evolving QFT on Lattice with Controllable Chaos by David Berenstein
Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to
From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography
On Bowen's equation for non-conformal repellers by Nuno Luzia
PROGRAM SMOOTH AND HOMOGENEOUS DYNAMICS ORGANIZERS: Anish Ghosh, Stefano Luzzatto and Marcelo Viana DATE: 23 September 2019 to 04 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases.
From playlist Smooth And Homogeneous Dynamics
From playlist Dimensions Arabe/Arabic / العربية
Ergodic optimization of Birkhoff averages and Lyapunov exponents – Jairo Bochi – ICM2018
Dynamical Systems and Ordinary Differential Equations Invited Lecture 9.9 Ergodic optimization of Birkhoff averages and Lyapunov exponents Jairo Bochi Abstract: We discuss optimization of Birkhoff averages of real or vectorial functions and of Lyapunov exponents of linear cocycles, empha
From playlist Dynamical Systems and ODE