On the Bernoulli property for rational maps

DOI10.1017/S0143385700002765zbMath0605.28011OpenAlexW1988821396MaRDI QIDQ3743546

Ricardo Mañé

Publication date: 1985

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385700002765

zbMATH Keywords

entropyrational functionanalytic endomorphism of the Riemann sphereone sided Bernoulli shift

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Ergodic theory (37A99)

Related Items (10)

Measures with positive Lyapunov exponent and conformal measures in rational dynamics ⋮ Undecidability and chaos in word-coded symbolic dynamics ⋮ On the Perron-Frobenius-ruelle operator for rational maps on the riemann sphere and for Hölder continuous functions ⋮ Fluctuations of ergodic sums on periodic orbits under specification ⋮ Fine inducing and equilibrium measures for rational functions of the Riemann sphere ⋮ Natural extensions for piecewise affine maps via Hofbauer towers ⋮ On some coding and mixing properties for a class of chaotic systems ⋮ Ergodic and Bernoulli properties of analytic maps of complex projective space ⋮ Measures and dimensions in conformal dynamics ⋮ Higher dimensional expanding maps and toral extensions

Cites Work

• Factors of Bernoulli shifts are Bernoulli shifts
• An invariant measure for rational maps
• On the uniqueness of the maximizing measure for rational maps

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