Determining consecutive periods of the Lorenz maps

DOI10.1155/2010/985982zbMath1417.37133OpenAlexW2168784813WikidataQ59253819 ScholiaQ59253819MaRDI QIDQ1957550

Fulai Wang

Publication date: 27 September 2010

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2010/985982

zbMATH Keywords

symbolic dynamicsLorenz mapsconsecutive periodic orbits

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25)

Cites Work

• A computer-assisted proof for the existence of horseshoe in a novel chaotic system
• Towards a computer-assisted proof for chaos in a forced damped pendulum equation
• A theorem of Sarkovskii on the existence of periodic orbits of continuous endomorphisms of the real line
• A computer proof that the Lorenz equations have ``chaotic solutions
• Predicting orbits of the Lorenz equation from symbolic dynamics
• Computer assisted proof of chaos in the Lorenz equations
• Dual star products and metric universality in symbolic dynamics of three letters.
• Period Three Implies Chaos
• Chaos in the Lorenz equations: A computer assisted proof. Part II: Details
• Deterministic Nonperiodic Flow
• Chaos in the Lorenz equations: A computer assisted proof. III: Classical parameter values
• Topological invariants and renormalization of Lorenz maps

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