The maximum-entropy measure of a rational endomorphism of the Riemann sphere

DOI10.1007/BF01077862zbMath0525.28021OpenAlexW2082145394MaRDI QIDQ594230

Mikhail Lyubich

Publication date: 1983

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01077862

zbMATH Keywords

dynamical systemrational functionstopological endomorphisms of the Riemann sphere

Mathematics Subject Classification ID

Entropy and other invariants (28D20) Entropy in general topology (54C70) Ergodic theory (37A99)

Related Items (10)

Distribution of typical orbits for random dynamics generated by finitely many rational maps ⋮ On amenability and measure of maximal entropy for semigroups of rational maps: II ⋮ On dynamics of asymptotically minimal polynomials ⋮ Self-similar groups and holomorphic dynamics: renormalization, integrability, and spectrum ⋮ Hyperbolic groupoids: metric and measure ⋮ q-plane zeros of the Potts partition function on diamond hierarchical graphs ⋮ On the speed of convergence of Newton’s method for complex polynomials ⋮ Lee-Yang-Fisher zeros for the DHL and 2D rational dynamics. II: Global pluripotential interpretation ⋮ Amenability and measure of maximal entropy for semigroups of rational maps ⋮ Computable Geometric Complex Analysis and Complex Dynamics

Cites Work

• Applications of almost periodic compactifications
• Invariant sets under iteration of rational functions
• Degenerate case of stability problem for viscoelastic bodies

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