Lectures related to Discrete Time Solution: Stability Properties and Fixed Points

Explores scaling and renormalization in statistical mechanics, emphasizing critical points and invariant properties.

Explores one-dimensional maps, periodic solutions, and bifurcations in dynamical systems.

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

Covers the stability of discrete time periodic solutions and their properties.

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.

Covers the basics of information theory, entropy, and fixed points in graph colorings and the Ising model.

Covers the Picard method for solving nonlinear equations using fixed point iteration.

Explores the Banach Fixed Point Theorem, showing the uniqueness of fixed points in contraction mappings.

Explores logistic maps, bifurcations, equilibrium points, and periodic orbits in nonlinear dynamics and chaos.

Explores fixed point stability, Lyapunov functions, Lotka-Volterra models, and nonlinear dynamics in complex systems.

Explores the convergence of fixed point methods and the implications of different convergence rates.

Covers the topic of nonlinear equations and the fixed point method.

Explores the Kuramoto model for synchronization in phase oscillators and discusses stability criteria and critical coupling values.

Explores bistability in genetic networks, analyzing fixed points and stability, phase portraits, and experimental implementation.

Explores the numerical analysis of nonlinear equations, focusing on convergence criteria and methods like bisection and fixed-point iteration.

Explores the Newton method for non-linear equations, discussing convergence criteria and stopping conditions.

Covers rotations around fixed points and spherical coordinates, discussing cinematic moments and angular velocity.

Covers dynamic systems, trajectories, growth models, stability of fixed points, and linearization of models.

Explores fixed points and their stability in dynamic systems, emphasizing linear stability analysis.

Covers the Newton method for finding zeros of functions using data interpolation.