Lectures related to Weakly Nonlinear Approach: Bifurcations and Amplitude Equations

Weakly Nonlinear Analysis: Multiple Time Scale Expansion

Explores weakly nonlinear analysis through multiple time scale expansion, emphasizing the period of a gravitational pendulum and non-resonance conditions.

Dynamical Systems: Maps and Stability

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

Dynamical Systems for Engineers

Covers the theoretical basis of linear and nonlinear dynamical systems for engineers.

Bifurcations: Introduction

Covers the introduction to bifurcations in dynamical systems, including examples and theorems.

Equilibrium Points and Bifurcations

Introduces equilibrium points and bifurcations in differential equations, discussing their stability and relevance in various contexts.

Fractional Response

Explores linear response in dynamical systems, emphasizing fractional derivatives and expanding unimodal maps.

Nonlinear Dynamics: Bifurcations and Stability

Explores nonlinear dynamics, bifurcations, stability, weakly nonlinear systems, saturation, Hopf bifurcation, and global stability analysis.

Nonlinear Dynamics and Chaos

Covers Hopf bifurcations, pitchfork bifurcations, and the Lorenz system in nonlinear dynamics and chaos.

Nonlinear Dynamics and Chaos

Covers bifurcations, long-term dynamics, logistic map, universality, and correspondence between different maps.

Nonlinear Dynamics: Homoclinic Orbits and Bifurcations

Delves into homoclinic orbits, bifurcations, and limit cycles in nonlinear dynamics.

Bifurcation and fractals in complex dynamical systems

Explores bifurcation, fractals, Julia sets, Mandelbrot set, and self-similarity in complex dynamical systems.

Introduction to Quantum Chaos

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

Transcritical Bifurcations: Understanding Dynamical Systems

Explores transcritical bifurcations and the dynamics near critical points.

Nonlinear Dynamics and Chaos

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

Stellar Orbits: Integrals of Motion and Phase Space Visualization

Covers integrals of motion and surfaces of section in stellar dynamics.

Dynamical System Theory: Bifurcations

Covers the topic of bifurcations in dynamical system theory, focusing on the pitchfork bifurcation.

Newton-Krylov-hookstep Methods

Covers Newton-Krylov-hookstep methods for finding roots of high-dimensional systems.

Fractional Susceptibility in Quadratic Dynamics

Explores the fractional susceptibility function in quadratic dynamical systems, highlighting its significance and the associated paradoxes in parameter dependence.

Stability Analysis: Linear Systems

Explores stability analysis in linear systems, emphasizing eigenvalues, eigenvectors, and stable manifolds.

Introduction to Dynamical System

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