By Sergey Bezuglyi,Sergiy Kolyada

This publication includes a selection of survey papers through top researchers in ergodic concept, low-dimensional and topological dynamics and it contains 9 chapters on a number of very important themes. those comprise: the position and usability of ultrafilters in ergodic conception, topological dynamics and Ramsey idea; topological points of kneading concept including a similar 2-dimensional concept referred to as pruning; the dynamics of Markov odometers, Bratteli-Vershik diagrams and orbit equivalence of non-singular automorphisms; geometric proofs of Mather's connecting and accelerating theorems; contemporary leads to one dimensional tender dynamics; periodic issues of nonexpansive maps; mathematics dynamics; the illness of issue maps; entropy concept for activities of countable amenable groups.

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