Elements of Applied Bifurcation Theory

1 Introduction to Dynamical Systems. - 2 Topological Equivalence Bifurcations and Structural Stability of Dynamical Systems. - 3 One-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems. - 4 One-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems. - 5 Bifurcations of Equilibria and Periodic Orbits in n-Dimensional Dynamical Systems. - 6 Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria. - 7 Other One-Parameter Bifurcations in Continuous-Time Dynamical Systems. - 8 Two-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems. - 9 Two-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems. - 10 Numerical Analysis of Bifurcations. - A Basic Notions from Algebra Analysis and Geometry. - A. 1 Algebra. - A. 1. 1 Matrices. - A. 1. 2 Vector spaces and linear transformations. - A. 1. 3 Eigenvectors and eigenvalues. - A. 1. 4 Invariant subspaces generalized eigenvectors and Jordan normal form. - A. 1. 5 FredholmAlternative Theorem. - A. 1. 6 Groups. - A. 2 Analysis. - A. 2. 1 Implicit and Inverse Function Theorems. - A. 2. 2 Taylor expansion. - A. 2. 3 Metric normed and other spaces. - A. 3 Geometry. - A. 3. 1 Sets. - A. 3. 2 Maps. - A. 3. 3 Manifolds. - References. Language: English