Statistical properties of chaos demonstrated in a class of one-dimensional maps
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Publication:4526268
DOI10.1063/1.165977zbMath1055.37535OpenAlexW2017842391WikidataQ73464315 ScholiaQ73464315MaRDI QIDQ4526268
P. Szépfalusy, András Csordás, Tamás Tél, Géza Györgyi
Publication date: 16 January 2001
Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.165977
Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Dynamical systems involving maps of the interval (37E05)
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Cites Work
- Spectrum and eigenfunctions of the Frobenius-Perron operator of the tent map
- The dimension spectrum of Axiom A attractors
- On the thermodynamic formalism for the Gauss map
- Some characterizations of strange sets
- Properties of fully developed chaos in one-dimensional maps
- Repellers, semi-attractors, and long-lived chaotic transients
- Toward a quantitative theory of self-generated complexity
- The entropy function for characteristic exponents
- Locating resonances for axiom A dynamical systems
- On the relaxation time of Gauss' continued-fraction map. I: The Hilbert space approach (Koopmanism)
- Absolutely continuous measures for certain maps of an interval
- Conditionally invariant measures and exponential decay
- Phase transitions in experimental systems
- Maps of intervals with indifferent fixed points: thermodynamic formalism and phase transitions
- Projection operator approach to the thermodynamic formalism of dynamical systems
- Phase transitions in thermodynamics of a local Lyapunov exponent for fully-developed chaotic systems
- Characteristic exponents of chaotic repellers as eigenvalues
- Presentation functions, fixed points, and a theory of scaling function dynamics.
- Generalized dimensions, entropies, and Lyapunov exponents from the pressure function for strange sets.
- Scaling laws for invariant measures on hyperbolic and nonhyperbolic attractors.
- Statistical Dynamics Generated by Fluctuations of Local Lyapunov Exponents
- The spectrum of the period-doubling operator in terms of cycles
- Hausdorff dimension for horseshoes
- Escape from strange repellers
- Recycling of strange sets: I. Cycle expansions
- Fractal measures and their singularities: The characterization of strange sets
- Characterisation of intermittency in chaotic systems
- A subadditive thermodynamic formalism for mixing repellers
- Sporadicity: Between periodic and chaotic dynamical behaviors
- A Variational Principle for the Pressure of Continuous Transformations
- Scaling structure and thermodynamics of strange sets
- Determination of correlation spectra in chaotic systems
- Ergodic theory of chaos and strange attractors
- Some properties of mixing repellers
- The Dimension Spectrum of the Maximal Measure
- Repellers for real analytic maps
- Crises, sudden changes in chaotic attractors, and transient chaos
- Universal f(α) spectrum as an eigenvalue