Forward generator for preimage entropy

Wen-Chiao Cheng

Vol. 223 (2006), No. 1, 5–16

DOI: 10.2140/pjm.2006.223.5

Abstract

We investigate preimage entropy and show how to calculate it under the assumption of forward expansiveness. We then define new invariants of noninvertible maps, called the upper preimage entropy and the metric preimage entropy, and obtain variational principles for them. Last, we prove a similar result for the Kolmogorov–Sinai generator.

Keywords

preimage entropy, forward generator, expansiveness

Mathematical Subject Classification 2000

Primary: 37B40

Milestones

Received: 25 April 2004

Revised: 2 February 2005

Accepted: 15 February 2005

Published: 1 January 2006