Recurrence in topological dynamics
Subtitle: Furstenberg families and Ellis actions
By: Ethan Akin.
Series: The university series in mathematics; University series in mathematics (Plenum Press)
Publisher: Plenum Press
Published: 1997
Place of publication: New York
Language: eng
Number of pages: 265
Subjects: Topological dynamics; Point mappings (Mathematics)
Description: A recurrent point for the dynamical system of a map is a point whose orbit returns arbitrarily close to its initial position infinitely often. Different sorts of recurrence can be described by keeping track of just how frequently these returns occur. By considering the case when these return time sets are in some family of special subsets of the natural numbers - for example, the syndetic sets or IP sets - we obtain the concept of recurrence associated with the family.

This groundbreaking volume is the first to elaborate the theory of set families as a tool for studying the phenomenon of recurrence. Though the theory is implicit in such seminal works as Hillel Furstenberg's Recurrence in Ergodic Theory and Combinatorial Number Theory (Princeton University Press, 1981), Ethan Akin's study expands upon the theory in detail and explicitly describes this useful piece of mathematical folklore.
Notes: Includes bibliographical references (p. 261-262) and index.