This book contains papers from two Chapel Hill Ergodic Theory
Workshops organized in February 2007 and 2008.
With material from the first year of the blog already published in book form, this book is the first volume of a two-volume set of blog posts from 2008, focusing on ergodic theory
, topological dynamics, combinatorics, and number theory.
for their brilliant and groundbreaking work in harmonic analysis, partial differential equations, ergodic theory
, number theory, combinatorics, functional analysis and theoretical computer science".
Objective: Built on decades of deep research in ergodic theory
, Szemeredi~s regularity theory and statistical physics, a new subject is emerging whose goal is to study convergence and limits of various structures.
Three surveys discuss ultraproducts of first order structures, set-theoretic aspects of ultrafilters, and connections with ergodic theory
Weiss, Ergodic theory
and configurations in sets of positive density, Mathematics of Ramsey Theory, 184-198, Algorithms Combi.
Objective: Ergodic theory
is the analysis of probabilistic or statistical aspects of deterministic systems.
With a wide range of unified, and in some cases significantly streamlined proofs of difficult results, including dichotomy theorems, this offers a fresh approach to the theory of Borel equivalence relations and related topics insect theory, ergodic theory
, topological dynamics, group theory, combinatorics, functional analysis, and model theory.
Shields, The Ergodic Theory
of Discrete Sample Path, American Mathematical Society, 1996.
Topics include conformal automorphisms of finitely connected regions, meromophic functions with two completely invariant domains, residual Julia sets of rational and transcendental functions, generalizations of uniformly normal families, fractal measures and ergodic theory
of transcendental meromorphic functions, and, of course, Baker domains.