Encyclopedia of Dynamical Systems
by D. Anosov, at al.
Publisher: Scholarpedia 2009
The encyclopedia covers differential equations, numerical analysis, bifurcations, topological dynamics, ergodic theory, hyperbolic dynamics, oscillators, synchronization, pattern formation, chaos, statistical mechanics, control theory, and applications.
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by A. T. Baraviera, R. Leplaideur, A. O. Lopes - arXiv
We review some basic notions in ergodic theory and thermodynamic formalism, as well as introductory results in the context of max-plus algebra, in order to exhibit some properties of equilibrium measures when temperature goes to zero.
by Arild Wikan - Bookboon
This book covers important topics like stability, hyperbolicity, bifurcation theory and chaos, topics which are essential to understand the behavior of nonlinear discrete dynamical systems. The theory is illuminated by examples and exercises.
by P. Rabier - Tata Institute of Fundamental Research
This set of lectures gives a synthetic exposition for the study of one-parameter bifurcation problems. By this, we mean the analysis of the structure of their set of solutions through the same type of general arguments in various situations.
by A. A. Martynyuk - Bookboon
The monograph presents a generalization of the well-known Lyapunov function method and related concepts to the matrix function case within the framework of systematic stability analysis of dynamical systems (differential equations).