Real topological entropy versus metric entropy for birational measure-preserving transformations

DOI10.1016/S0167-2789(00)00079-8zbMath0978.37036OpenAlexW2098972335WikidataQ127644532 ScholiaQ127644532MaRDI QIDQ1587683

J.-Ch. Anglès D'Auriac, Nina Abarenkova, Jean-Marie Maillard, Salah Boukraa

Publication date: 3 December 2000

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(00)00079-8

zbMATH Keywords

entropyHénon mapLyapunov exponentArnold complexity

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50) Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems (37B35) Dynamical systems over complex numbers (37F99)

Related Items (6)

Using discrete Darboux polynomials to detect and determine preserved measures and integrals of rational maps ⋮ Noetherian mappings ⋮ Dynamics of a two parameter family of plane birational maps: maximal entropy ⋮ Degree complexity of a family of birational maps ⋮ Laminar currents and birational dynamics ⋮ Arithmetical Method to Detect Integrability in Maps

Cites Work

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• Polynomial diffeomorphisms of \(\mathbb{C}^ 2\). IV: The measure of maximal entropy and laminar currents
• The infinite number of generalized dimensions of fractals and strange attractors
• Universal behaviour in families of area-preserving maps
• A two-dimensional mapping with a strange attractor
• Dimensions and entropies of strange attractors from a fluctuating dynamics approach
• Entropy and twisted cohomology
• Structurally stable systems
• Volume growth and entropy
• \(C^ k\)-resolution of semialgebraic mappings, addendum to volume growth and entropy
• Non-expansive Hénon maps
• An upper estimation for topological entropy of diffeomorphisms
• Some relations between dimension and Lyapunov exponents
• Entropy of polynomial and rational maps
• Points périodiques d'applications birationnelles de \({\mathbb P}^2\). (Periodic points for birational mappings of \({\mathbb P}^2\).)
• Non-algebraic integrability of the Chew-Low reversible dynamical system of the Cremona type and the relation with the 7th Hilbert problem (non-resonant case)
• Algebraic-geometry approach to integrability of birational plane mappings. Integrable birational quadratic reversible mappings. I
• Polynomial diffeomorphisms of \({\mathbb{C}}^2\). V: Critical points and Lyapunov exponents
• Birational maps, positive currents, and dynamics.
• Discrete symmetry groups of vertex models in statistical mechanics.
• Growth-complexity spectrum of some discrete dynamical systems
• Quantitative universality for a class of nonlinear transformations
• Holomorphic symplectomorphisms in \(\mathbb{C}^{2p}\)
• Topological entropy and Arnold complexity for two-dimensional mappings
• Analytic transformations of \((\mathbb{C}^p,0)\) tangent to the identity
• On periodic points
• On the nature of turbulence
• Note concerning our paper On the nature of turbulence. Commun. math. Phys. 20, 167-192 (1971)
• Dimension, entropy and Lyapunov exponents
• Entropy and volume
• Dynamical systems, filtrations and entropy
• CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
• Periodic orbits and dynamical spectra (Survey)
• ALMOST INTEGRABLE MAPPINGS
• Dynamics of birational maps of P^2
• Value distribution for sequences of rational mappings and complex dynamics
• Real Arnold complexity versus real topological entropy for birational transformations
• Ergodic theory of chaos and strange attractors
• Deterministic Nonperiodic Flow
• Symbolic Dynamics for Hyperbolic Flows
• Topological Entropy
• Simple mathematical models with very complicated dynamics
• Differentiable dynamical systems
• Markov Partitions for Axiom A Diffeomorphisms
• Periodic Orbits for Hyperbolic Flows
• Chaos
• Probleme General de la Stabilite du Mouvement. (AM-17)
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

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