Fiber entropy and algorithmic complexity of random orbits

DOI10.3934/dcds.2022098OpenAlexW3198267366MaRDI QIDQ2676615

Elias Zimmermann

Publication date: 28 September 2022

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.13019

zbMATH Keywords

conditional Kolmogorov complexityrandom dynamicsfiber entropystep skew productstransformation bundles

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Algorithmic information theory (Kolmogorov complexity, etc.) (68Q30) Entropy and other invariants (28D20) Measures of information, entropy (94A17) Topological entropy (37B40) Random iteration (37H12)

Cites Work

• Brudno's theorem for \(\mathbb{Z}^d\) (or \(\mathbb{Z}_+^d\)) subshifts
• Entropy and algorithmic complexity in quantum information theory
• Effective symbolic dynamics, random points, statistical behavior, complexity and entropy
• Entropy of random dynamical systems
• Skew products and ergodic theorems for group actions
• Ergodic theorems for actions of free groups and free semigroups
• The Shannon-McMillan-Breiman theorem beyond amenable groups
• An announce of results linking Kolmogorov complexity to entropy for amenable group actions
• Symbolic dynamics: entropy = dimension = complexity
• Entropy and quantum Kolmogorov complexity: a quantum Brudno's theorem
• Asymptotic orbit complexity of infinite measure preserving transformations
• Algorithmic Randomness and Complexity
• Algorithmic complexity of points in dynamical systems
• Examples in the entropy theory of countable group actions
• Computable Følner monotilings and a theorem of Brudno
• Markov Chains, Skew Products and Ergodic Theorems for “General” Dynamic Systems
• Ergodic Theory
• Operator ergodic theorems for actions of free semigroups and groups
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