In the theory of ordinary differential equations (ODEs), Lyapunov functions, named after Aleksandr Lyapunov, are scalar functions that may be used to prove the stability of an equilibrium of an ODE. Lyapunov functions (also called Lyapunov’s second method for stability) are important to stability theory of dynamical systems and control theory. A similar concept appears in the theory of general state space Markov chains, usually under the name Foster–Lyapunov functions. For certain classes of ODEs, the existence of Lyapunov functions is a necessary and sufficient condition for stability. Whereas there is no general technique for constructing Lyapunov functions for ODEs, in many specific cases the construction of Lyapunov functions is known. For instance, quadratic functions suffice for systems with one state; the solution of a particular linear matrix inequality provides Lyapunov functions for linear systems; and conservation laws can often be used to construct Lyapunov functions for physical systems. (Wikipedia).
Transcendental Functions 19 The Function a to the power x.mp4
The function a to the power x.
From playlist Transcendental Functions
Introduction to Linear Functions and Slope (L10.1)
This lesson introduces linear functions, describes the behavior of linear function, and explains how to determine the slope of a line given two points. Video content created by Jenifer Bohart, William Meacham, Judy Sutor, and Donna Guhse from SCC (CC-BY 4.0)
From playlist Introduction to Functions: Function Basics
(New Version Available) Inverse Functions
New Version: https://youtu.be/q6y0ToEhT1E Define an inverse function. Determine if a function as an inverse function. Determine inverse functions. http://mathispower4u.wordpress.com/
From playlist Exponential and Logarithmic Expressions and Equations
Define linear functions. Use function notation to evaluate linear functions. Learn to identify linear function from data, graphs, and equations.
From playlist Algebra 1
Transcendental Functions 3 Examples using Properties of Logarithms.mov
Examples using the properties of logarithms.
From playlist Transcendental Functions
Transcendental Functions 17 The Indefinite Integral of 1 over u du Example 1.mov
Example problems involving the integral of u to the power negative 1 du.
From playlist Transcendental Functions
Transcendental Functions 13 Derivatives of a Function and its Inverse.mov
The first derivative of a function and the inverse of that function.
From playlist Transcendental Functions
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
Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
Lyapunov's Fractal (that Lyapunov knew nothing about) #SoME2
Hi everyone! I hope you enjoy my first video. I've known about Markus-Lyapunov Fractals for a few years now, and it surprised me that I couldn't find any video explaining how they work - so I thought I'd take a stab at it myself! This is also my submission for Summer of Math Exposition 2.
From playlist Summer of Math Exposition 2 videos
Aaron Ames: "Safety-Critical Control of Autonomous Systems"
Mathematical Challenges and Opportunities for Autonomous Vehicles 2020 Workshop II: Safe Operation of Connected and Autonomous Vehicle Fleets "Safety-Critical Control of Autonomous Systems" Aaron Ames - California Institute of Technology Abstract: Guaranteeing safe behavior is a critical
From playlist Mathematical Challenges and Opportunities for Autonomous Vehicles 2020
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
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
Anton Arnold: Modal based hypocoercivity methods on the torus and the real line with application...
CIRM VIRTUAL EVENT Recorded during the meeting "Kinetic Equations: from Modeling, Computation to Analysis" the March 22, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide m
From playlist Virtual Conference
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
Lyapunov equation and positivity in open quantum systems by Archak Purkayastha
Non-Hermitian Physics - PHHQP XVIII DATE: 04 June 2018 to 13 June 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore Non-Hermitian Physics-"Pseudo-Hermitian Hamiltonians in Quantum Physics (PHHQP) XVIII" is the 18th meeting in the series that is being held over the years in Quantum Phys
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On a local Lyapunov function for the McKean-Vlasov dynamics by Rajesh Sundaresan
Large deviation theory in statistical physics: Recent advances and future challenges DATE: 14 August 2017 to 13 October 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru Large deviation theory made its way into statistical physics as a mathematical framework for studying equilibrium syst
From playlist Large deviation theory in statistical physics: Recent advances and future challenges
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