Hyperbolic Manifolds, Discrete Groups and Ergodic Theory
by Curtis T. McMullen
Publisher: Harvard University 2011
Number of pages: 118
Contents: Ergodic theory; Dynamics on hyperbolic surfaces; Orbit counting, equidistribution and arithmetic; Spectral theory; Mixing of unitary representations of SLnR; Amenability; The Laplacian; All unitary representations of PSL2(R); Kazhdan's property T; Ergodic theory at infinity of hyperbolic manifolds; Lattices: Dimension 1; Dimension 2; Lattices, norms and totally real fields; Dimension 3; Dimension 4, 5, 6; Higher rank dynamics on the circle; The discriminant-regulator paradox.
Home page url
Download or read it online for free here:
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.
by Thomas Ward - University of East Anglia
These notes cover a very short introduction to measure-theoretic and topological entropy, and are aimed at understanding part of Yuzvinskii's formula for the entropy of compact group automorphisms. Based on a course at the Ohio State University.
by Gerald Teschl - Universitaet Wien
This book provides an introduction to ordinary differential equations and dynamical systems. We start with some simple examples of explicitly solvable equations. Then we prove the fundamental results concerning the initial value problem.