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Reduced dynamical systems

Part of: Ergodic theory Complex dynamical systems

Published online by Cambridge University Press:  26 May 2020

LUKA BOC THALER  and
UROŠ KUZMAN
LUKA BOC THALER
Affiliation:
Dipartimento Di Matematica, Università di Roma ‘Tor Vergata’, Italy email [email protected]
UROŠ KUZMAN
Affiliation:
Faculty of Mathematics and Physics, University of Ljubljana, Slovenia Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia email [email protected]
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Abstract

We consider the dynamics of complex rational maps on $\widehat{\mathbb{C}}$. We prove that, after reducing their orbits to a fixed number of positive values representing the Fubini–Study distances between finitely many initial elements of the orbit and the origin, ergodic properties of the rational map are preserved.

Keywords

low dimensional dynamicsclassical ergodic theoryrational functions

MSC classification

Primary: 37F10: Polynomials; rational maps; entire and meromorphic functions 37A35: Entropy and other invariants, isomorphism, classification
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 6 , June 2021 , pp. 1612 - 1626
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Copyright
© The Author(s) 2020. Published by Cambridge University Press

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