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The Ergodic Theory of Lattice Subgroups (AM-172)by Alexander Gorodnik; Amos Nevo
Princeton University Press 2009; US$ 37.50The results established in this book constitute a new departure in ergodic theory and a significant expansion of its scope. Traditional ergodic theorems focused on amenable groups, and relied on the existence of an asymptotically invariant sequence in the group, the resulting maximal inequalities based on covering arguments, and the transference principle. Here, Alexander Gorodnik and Amos Nevo develop a systematic general approach to the proof of ergodic theorems for a large class of non-amenable locally compact groups and their lattice subgroups. Simple general conditions on the spectral theory of the group and the regularity of the averaging sets are formulated, which suffice to guarantee convergence to the ergodic mean. In particular,... more...
An Outline of Ergodic Theoryby Steven Kalikow; Randall McCutcheon
Cambridge University Press 2010; US$ 48.00An engaging introduction to ergodic theory for graduate students, and a useful reference for the professional mathematician. more...
The Ergodic Theory of Discrete Groupsby Peter J. Nicholls
Cambridge University Press 1989; US$ 70.00The particular focus of the book is on the remarkable measure supported on the limit set of a discrete group that was first developed by S. J. Patterson. more...
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