After attending this class students are familiar with the basic concepts of dynamical bifurcation theory. They understand the behavior of differential and difference equations under parameter variations. Note that the class will be elementary and does NOT require previous knowledge on Dynamical Systems. 

Presentation at the blackboard.

1 Ordinary differential equations1.1 Basics (stability theory and parameter-dependent equations)1.2 Continuation of equilibria1.3 Bifurcation of equilibria (fold, transcritical and pitchfork bifurcation)1.4 Bifurcation of periodic solutions1.5 Center manifold theory (approximation of center manifolds, center manifolds in bifurcation theory)2 Difference equations2.1 Basics (stability theory and parameter-dependent equations)2.2 Continuation of periodic points2.3 Bifurcation of periodic points (fold, transcritical, pitchfork and flip bifurcation)2.4 Sacker-Neimark bifurcation2.5 Center manifold theory (approximation of center manifolds, center manifolds in bifurcation theory)

The course covers elementary topics and therefore only relies on Analysis 1--2, Linear Algebra (Jordan canonical form) and Ordinary Differential Equations. Preliminaries on Dynamical Systems are NOT required. 

H. Amann, Ordinary differential equations, de Gruyter, New York etc., 1990B. Aulbach, Gewöhnliche Differenzialgleichungen, Spektrum Akademischer Verlag, Heidelberg, 2004A. Homburg, J. Knobloch, Bifurcation theory, AMS, Providence RI, 2024Y. Kuznetsov, Elements of applied bifurcation theory (4th edition), Springer, Berlin etc. 2023

Oral exam on appointment

Contents of the class