In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance. In dynamical systems, an orbit is called Lyapunov stable if the forward orbit of any point is in a small enough neighborhood or it stays in a small (but perhaps, larger) neighborhood. Various criteria have been developed to prove stability or instability of an orbit. Under favorable circumstances, the question may be reduced to a well-studied problem involving eigenvalues of matrices. A more general method involves Lyapunov functions. In practice, any one of a number of different stability criteria are applied. (Wikipedia).
Stability Analysis, State Space - 3D visualization
Introduction to Stability and to State Space. Visualization of why real components of all eigenvalues must be negative for a system to be stable. My Patreon page is at https://www.patreon.com/EugeneK
From playlist Physics
What Is The Uncertainty Principle?
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From playlist Science Unplugged: Quantum Mechanics
Notwithstanding the fact that I introduce the topic as the orbit stabilizer syndrome, this video takes you through the orbit stabilizer theorem. :-) It states that the number of cosets formed by the stabilizer of a group (called the index) is the same as the number of elements in the orbi
From playlist Abstract algebra
Everything You Need to Know About Control Theory
Control theory is a mathematical framework that gives us the tools to develop autonomous systems. Walk through all the different aspects of control theory that you need to know. Some of the concepts that are covered include: - The difference between open-loop and closed-loop control - How
From playlist Control Systems in Practice
Laskar Jacques "Stability and Chaos in the Solar System. From Poincaré to the present"
Résumé Some of the most famous works of Henri Poincaré have been motivated by the problem of the stability of the Solar System. Indeed, since its formulation by Newton, this problem has fascinated astronomers and mathematicians, searching to prove the stability of the Solar System. Poinca
From playlist Colloque Scientifique International Poincaré 100
Courses - G. JONA LASINIO “Macroscopic Fluctuation Theory”
Stationary non-equilibrium states describe steady flows through macroscopic systems. Although they represent the simplest generalization of equilibrium states, they exhibit a variety of new phenomena. Within a statistical mechanics approach, these states have been the subject of several th
From playlist T1-2015 : Disordered systems, random spatial processes and some applications
Stabilizer in abstract algebra
In the previous video we looked at the orbit of a set. To work towards the orbit stabilizer theorem, we take a look at what a stabilizer is in this video.
From playlist Abstract algebra
Efficient Stability for the Weyl-Heisenberg Group - Thomas Vidick
Marston Morse Lectures Topic: Efficient Stability for the Weyl-Heisenberg Group Speaker: Thomas Vidick Affiliation: California Institute of Technology Date: March 31, 2023 The question of stability of approximate group homomorphisms was first formulated by Ulam in the 1940s. One of the m
From playlist Mathematics
Stability and Periodicity in Modular Representation Theory - Nate Harman
Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: Stability and Periodicity in Modular Representation Theory Speaker: Nate Harman Affiliation: Member, School of Mathematics Date: November 18, 2020 For more video please visit http://video.ias.edu
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory
Mechanisms for Inflation, part 3 - Eva Silverstein
Mechanisms for Inflation, part 3 Eva Silverstein Stanford University July 21, 2011
From playlist PiTP 2011
Stability conditions in symplectic topology – Ivan Smith – ICM2018
Geometry Invited Lecture 5.8 Stability conditions in symplectic topology Ivan Smith Abstract: We discuss potential (largely speculative) applications of Bridgeland’s theory of stability conditions to symplectic mapping class groups. ICM 2018 – International Congress of Mathematicians
From playlist Geometry
Felix Klein Lectures 2020: Quiver moduli and applications, Markus Reineke (Bochum), Lecture 4
Quiver moduli spaces are algebraic varieties encoding the continuous parameters of linear algebra type classification problems. In recent years their topological and geometric properties have been explored, and applications to, among others, Donaldson-Thomas and Gromov-Witten theory have
From playlist Felix Klein Lectures 2020: Quiver moduli and applications, Markus Reineke (Bochum)
Maxim Kontsevich - New Life of D-branes in Math
One of the most wonderful gifts from string theory to pure mathematics comes from Mike Douglas' ideas on the decay of D-branes and walls of marginal stability. Tom Bridgeland formalized structures discovered by Mike as stability conditions in abstract triangulated categories. This notion b
From playlist Mikefest: A conference in honor of Michael Douglas' 60th birthday
Applications of Chiral Kinetic Theory by Naoki Yamamoto
DISCUSSION MEETING EXTREME NONEQUILIBRIUM QCD (ONLINE) ORGANIZERS: Ayan Mukhopadhyay (IIT Madras) and Sayantan Sharma (IMSc Chennai) DATE & TIME: 05 October 2020 to 09 October 2020 VENUE: Online Understanding quantum gauge theories is one of the remarkable challenges of the millennium
From playlist Extreme Nonequilibrium QCD (Online)
Richard Thomas - Vafa-Witten Invariants of Projective Surfaces 3/5
1. Sheaves, moduli and virtual cycles 2. Vafa-Witten invariants: stable and semistable cases 3. Techniques for calculation --- virtual degeneracy loci, cosection localisation and a vanishing theorem 4. Refined Vafa-Witten invariants
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Stephen GUSTAFSON - Stability of periodic waves of 1D nonlinear Schrödinger equations
Motivated by the more general problem of classifying NLS dynamics in the presence of a potential, we consider the case of a (suitably) small, repulsive potential, and for certain nonlinearities, classify solutions near the 'pinned' ground state according to classical trajectories. Joint wo
From playlist Trimestre "Ondes Non linéaires" - Summer school
The Seduction of Curves: The Lines of Beauty That Connect Mathematics, Art and The Nude
Oxford Mathematics Public Lectures: Allan McRobie - The Seduction of Curves: The Lines of Beauty That Connect Mathematics, Art and The Nude There is a deep connection between the stability of oil rigs, the bending of light during gravitational lensing and the act of life drawing. To unde
From playlist Oxford Mathematics Public Lectures
Some questions around quasi-periodic dynamics – Bassam Fayad & Raphaël Krikorian – ICM2018
Dynamical Systems and Ordinary Differential Equations Invited Lecture 9.2 Some questions around quasi-periodic dynamics Bassam Fayad & Raphaël Krikorian Abstract: We propose in these notes a list of some old and new questions related to quasi-periodic dynamics. A main aspect of quasi-per
From playlist Dynamical Systems and ODE
Equilibrium Solutions and Stability of Differential Equations (Differential Equations 36)
https://www.patreon.com/ProfessorLeonard Exploring Equilibrium Solutions and how critical points relate to increasing and decreasing populations.
From playlist Differential Equations