Functional analysis | Dynamical systems
In applied mathematics and dynamical system theory, Lyapunov vectors, named after Aleksandr Lyapunov, describe characteristic expanding and contracting directions of a dynamical system. They have been used in predictability analysis and as initial perturbations for ensemble forecasting in numerical weather prediction. In modern practice they are often replaced by bred vectors for this purpose. (Wikipedia).
Vector Calculus 1: What Is a Vector?
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Vector Calculus
Particles starting near positive-time LCS attract onto negative-time LCS (zoom out)
This video depicts particles that start near the positive-time Lagrangian coherent structure (LCS) attract onto negative-time LCS as they are integrated forward in time. The flow field corresponds to a pitching flat plate at low Reynolds number (Re=100). This movie corresponds to Fig. 11
From playlist Finite-time Lyapunov exponents
Particles starting near positive-time LCS attract onto negative-time LCS
This video depicts particles that start near the positive-time Lagrangian coherent structure (LCS) attract onto negative-time LCS as they are integrated forward in time. The flow field corresponds to a pitching flat plate at low Reynolds number (Re=100). This movie corresponds to Fig. 11
From playlist Finite-time Lyapunov exponents
This shows an small game that illustrates the concept of a vector. The clip is from the book "Immersive Linear Algebra" at http://www.immersivemath.com
From playlist Chapter 2 - Vectors
Charles Favre: Explosion of Lyapunov exponents using non-Archimedean geometry
Abstract: We consider a meromorphic family of endomorphisms of the complex projective space parameterized by the unit disk, and show that the blow-up of the Lyapunov exponent near the origin is controlled by a non-Archimedean quantity. Recording during the thematic meeting : "p-adic Analy
From playlist Algebraic and Complex Geometry
Now we know about vector spaces, so it's time to learn how to form something called a basis for that vector space. This is a set of linearly independent vectors that can be used as building blocks to make any other vector in the space. Let's take a closer look at this, as well as the dimen
From playlist Mathematics (All Of It)
Large coupling asymptotics for the Lyapunov...with analytic potentials -Christoph Marx
Analysis Math-Physics Seminar Topic: Reinforced random walks and statistical physics Speaker: Christoph Marx Affiliation: Oberlin College Date: Wednesday, January 25 For more video, visit http://video.ias.edu
From playlist Mathematics
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
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
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
Chaotic properties of spin lattices at high temperatures by Boris V. Fine
PROGRAM THERMALIZATION, MANY BODY LOCALIZATION AND HYDRODYNAMICS ORGANIZERS: Dmitry Abanin, Abhishek Dhar, François Huveneers, Takahiro Sagawa, Keiji Saito, Herbert Spohn and Hal Tasaki DATE : 11 November 2019 to 29 November 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore How do is
From playlist Thermalization, Many Body Localization And Hydrodynamics 2019
Amir Ali Ahmadi, Princeton University
January 31, Amir Ali Ahmadi, Princeton University Two Problems at the Interface of Optimization and Dynamical Systems We propose and/or analyze semidefinite programming-based algorithms for two problems at the interface of optimization and dynamical systems: In part (i), we study the po
From playlist Spring 2020 Kolchin Seminar in Differential Algebra
Algorithmic Lie Symmetry Analysis and Group Classification for Ordinary Differential Equations
From playlist Spring 2018
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
Visualization of tensors - part 1
This video visualizes tensors. It shows some introduction to tensor theory and demonstrates it with the Cauchy stress tensor. Future parts of this series will show more theory and more examples. It talks about the term 'tensor' as used in physics and math. In the field of AI the term 'te
From playlist Animated Physics Simulations
Lagrangian Coherent Structures (LCS) in unsteady fluids with Finite Time Lyapunov Exponents (FTLE)
Fluid dynamics are often characterized by coherent structures that persist in time and mediate the behavior and transport of the fluid. Lagrangian coherent structures (LCS) are a particularly important class of coherent structures, as they are the time-varying analogues of stable and unst
From playlist Data Driven Fluid Dynamics
Lyapunov exponents for small random perturbations… - Alex Blumenthal
Symplectic Dynamics/Geometry Seminar Topic: Lyapunov exponents for small random perturbations of predominantly hyperbolic two dimensional volume-preserving diffeomorphisms, including the Standard Map Speaker: Alex Blumenthal Affiliation: University of Maryland Date: November 19, 2018 For
From playlist Mathematics
Continuity of Lyapunov exponents for non-uniformly fiber-bunched linear cocycles by Catalina Freijo
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
A short refresher on vectors. Before I introduce vector-based functions, it's important to look at vectors themselves and how they are represented in python™ and the IPython Notebook using SymPy.
From playlist Life Science Math: Vectors