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Preimage pressure for random transformations

Published online by Cambridge University Press:  03 February 2009

YUJUN ZHU ,
ZHIMING LI  and
XIAOHONG LI
YUJUN ZHU
Affiliation:
College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050016, People’s Republic of China (email: yjzhu@mail.hebtu.edu.cn, china-lizhiming@163.com, helen519@163.com)
ZHIMING LI
Affiliation:
College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050016, People’s Republic of China (email: yjzhu@mail.hebtu.edu.cn, china-lizhiming@163.com, helen519@163.com)
XIAOHONG LI
Affiliation:
College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050016, People’s Republic of China (email: yjzhu@mail.hebtu.edu.cn, china-lizhiming@163.com, helen519@163.com)
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Abstract

In this paper, preimage pressure, which is based on the preimage structure of the system, is defined and studied for random transformations. We obtain analogs of many known results of preimage entropy and preimage pressure for deterministic cases in Cheng and Newhouse [Pre-image entropy. Ergod. Th. & Dynam. Sys.25 (2005), 1091–1113] and Zeng et al [Pre-image pressure and invariant measures. Ergod. Th. & Dynam. Sys.27 (2007), 1037–1052]. In particular, a variational principle is given and some applications of preimage pressure, such as the investigation of the invariant measures and the equilibrium states, are obtained.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 5 , October 2009 , pp. 1669 - 1687
Copyright
Copyright © Cambridge University Press 2009

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