Author | Kuznetsov, Yuri A. author |
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Title | Elements of Applied Bifurcation Theory [electronic resource] / by Yuri A. Kuznetsov |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2004 |
Edition | Third Edition |
Connect to | http://dx.doi.org/10.1007/978-1-4757-3978-7 |
Descript | XXII, 632 p. online resource |
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 Fredholm Alternative 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