Lectures related to Small Scale Stability: Gradient Systems

Dynamical Systems: Equilibrium Points and Stability

Covers dynamical systems, equilibrium points, stability analysis, and phase plots using examples like the pendulum system.

Small Scale Stability: Gradient Systems

Covers small scale stability in gradient systems, focusing on trajectory properties and equilibrium point attraction.

Introduction to Dynamical System

Introduces dynamical systems, equilibrium points, stability, vector fields, phase plots, and Lyapunov stability.

Dynamical System Theory for Engineers: Large Scale Stability

Covers the concept of large scale stability in dynamical systems.

Dynamical System Theory for Engineers: Large Scale Stability

Explores large scale stability in dynamical systems, emphasizing non-increasing trajectories and strict decrease of a specific function.

Introduction to Quantum Chaos

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Compact Sets and Extreme Values

Explores compact sets, extreme values, and function theorems on bounded sets.

Chaos and Lyapunov Exponents: Analyzing Predictability

Covers Lyapunov exponents, chaos measurement, and perturbation analysis in dynamical systems.

Lyapunov II: Stability and Invariance

Explores Lyapunov stability and invariance of dynamical systems through examples and corollaries.

Introduction to Dynamical System Theory for Engineers

Covers trajectory, solution, and orbit of dynamical systems for engineers.

Periodic Orbits of Hamiltonian Systems

Covers Morse theory, critical points, and Conley-Zehnder index in Hamiltonian systems.

Large Scale Stability Analysis

Covers large scale stability analysis and properties of dynamical systems solutions.

Small Scale Stability: Equilibrium Point

Covers small scale stability at equilibrium points in dynamical systems for engineers.

Lyapunov Stability in Dynamical Systems

Covers Lyapunov stability in dynamical systems, focusing on global asymptotic stability and practical implementation through semidefinite programming.

Mild Dissipative Surface Dynamics

Explores mild dissipative surface dynamics, including conservative behavior and ergodic functions.

Quantum Chaos and Scrambling

Explores the concept of scrambling in quantum chaotic systems, connecting classical chaos to quantum chaos and emphasizing sensitivity to initial conditions.

Compact Embedding: Theorem and Sobolev Inequalities

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Mathematical Modeling in Chemistry and Biology

Covers mathematical modeling in chemistry and biology, including chemical reactions, enzymatic kinetics, and population dynamics.

Lyapunov Stability and Chebyshev Inequalities

Explores Lyapunov stability and Chebyshev inequalities in system analysis and control design.

Learning and Adaptive Control for Robots: SEDS & LPV-DS

Explores learning and adaptive control for robots through SEDS and LPV-DS, emphasizing stability, non-linear dynamics, and optimization.