Dynamics, Ergodic Theory, and Geometry
by Boris Hasselblatt
Publisher: Cambridge University Press 2007
Number of pages: 334
This volume contains surveys and research articles by leading experts in several areas of dynamical systems that have recently experienced substantial progress. Some of the major surveys focus on symplectic geometry; smooth rigidity; hyperbolic, parabolic, and symbolic dynamics; and ergodic theory. Students and researchers in dynamical systems, geometry, and related areas will find this a fascinating look at the state of the art.
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by Alexey Shabat, Elena Kartashova - arXiv
A preliminary version of the textbook on integrable systems. Contents: General notions and ideas; Riccati equation; Factorization of linear operators; Commutativity of linear operators; Integrability of non-linear PDEs; Burgers-type equations.
by Claudius Gros - arXiv
This textbook covers a wide range of concepts, notions and phenomena of a truly interdisciplinary subject. Complex system theory deals with dynamical systems containing a very large number of variables, showing a plethora of emergent features.
by Shlomo Sternberg - OER Commons
This book addresses the following topics: Iterations and fixed points; bifurcations; conjugacy; space and time averages; the contraction fixed point theorem; Hutchinson's theorem and fractal images; hyperbolicity; and symbolic dynamics.
by D. Anosov, at al. - Scholarpedia
The encyclopedia covers differential equations, numerical analysis, bifurcations, topological dynamics, ergodic theory, hyperbolic dynamics, oscillators, pattern formation, chaos, statistical mechanics, control theory, and applications.