Erratum to ‘Semi-hyperbolic fibered rational maps and rational semigroups’ (Ergodic Theory and Dynamical Systems 26 (2006), 893–922)

2008 ◽  
Vol 28 (3) ◽  
pp. 1043-1045 ◽  
Author(s):  
HIROKI SUMI
Keyword(s):  
Dynamical Systems ◽  
Ergodic Theory ◽  
Rational Maps

AbstractWe give a correction to the assumption of Theorems 1.12 and 2.6 in the paper [H. Sumi. Semi-hyperbolic fibered rational maps and rational semigroups. Ergod. Th. & Dynam. Sys.26 (2006), 893–922].

scholarly journals Category Theory for Autonomous and Networked Dynamical Systems

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 302 ◽  
Author(s):  
Jean-Charles Delvenne
Keyword(s):  
Dynamical Systems ◽  
Systems Theory ◽  
Ergodic Theory ◽  
Category Theory ◽  
Open Systems ◽  
Topological Dynamics ◽  
Control Problems ◽  
Natural Conditions ◽  
Discussion Paper ◽  
Open Systems Theory

In this discussion paper we argue that category theory may play a useful role in formulating, and perhaps proving, results in ergodic theory, topogical dynamics and open systems theory (control theory). As examples, we show how to characterize Kolmogorov–Sinai, Shannon entropy and topological entropy as the unique functors to the nonnegative reals satisfying some natural conditions. We also provide a purely categorical proof of the existence of the maximal equicontinuous factor in topological dynamics. We then show how to define open systems (that can interact with their environment), interconnect them, and define control problems for them in a unified way.

Dynamical Systems, Ergodic Theory and Applications

2000 ◽  
Vol 84 (501) ◽  
pp. 573
Author(s):  
Steve Abbott ◽  
Ya. G. Sinai
Keyword(s):  
Dynamical Systems ◽  
Ergodic Theory

New developments in the ergodic theory of nonlinear dynamical systems

1994 ◽  
Vol 346 (1679) ◽  
pp. 145-157 ◽  
Keyword(s):  
Dynamical Systems ◽  
Ergodic Theory ◽  
Nonlinear Dynamical Systems ◽  
Statistical Properties ◽  
Strange Attractors ◽  
New Developments ◽  
Nonlinear Dynamical ◽  
Henon Maps ◽  
Open Questions ◽  
Hyperbolic Dynamical Systems

The purpose of this paper is to give a survey of recent results on non-uniformly hyperbolic dynamical systems. The emphasis is on the existence of strange attractors and Sinai-Ruelle-Bowen measures for Henon maps, but we also describe results about statistical properties of such dynamical systems and state some of the open questions in this area.

scholarly journals Ergodic theory for Markov fibred systems and parabolic rational maps

1993 ◽  
Vol 337 (2) ◽  
pp. 495-548 ◽  
Author(s):  
Jon Aaronson ◽  
Manfred Denker ◽  
Mariusz Urbański
Keyword(s):  
Ergodic Theory ◽  
Rational Maps
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