Nonlinear Dynamics: Homoclinic Orbits and Bifurcations

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

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

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

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

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

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

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

Explores the composition of applications in mathematics and the importance of understanding their properties.

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.