What you need to know to knead

DOI10.1016/0001-8708(89)90033-9zbMath0701.58032OpenAlexW2027226287WikidataQ61632431 ScholiaQ61632431MaRDI QIDQ914219

Chris Preston

Publication date: 1989

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(89)90033-9

zbMATH Keywords

entropyzeta functionkneading theoryiterated mapspiecewise monotone mapsgrowth numberkneading determinantkneading matrix

Mathematics Subject Classification ID

Topological dynamics (37B99) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Iteration of real functions in one variable (26A18) Ergodic theory (37A99)

Related Items (16)

Detecting topological transitivity of piecewise monotone interval maps ⋮ RELATION BETWEEN KNEADING MATRICES OF A MAP AND ITS ITERATES ⋮ Networks Synchronizability, Local Dynamics and Some Graph Invariants ⋮ TOPOLOGICAL ENTROPY IN THE SYNCHRONIZATION OF PIECEWISE LINEAR AND MONOTONE MAPS: COUPLED DUFFING OSCILLATORS ⋮ Eigenfunctions of the Perron–Frobenius operators for generalized beta-maps ⋮ Spectral properties of a class of operators associated with maps in one dimension ⋮ The zeta function of the beta transformation ⋮ Kneading with weights ⋮ An extension of the theorem of Milnor and Thurston on the zeta functions of interval maps ⋮ Zeta functions and transfer operators for piecewise monotone transformations ⋮ The lap-counting function for linear mod one transformations I: explicit formulas and renormalizability ⋮ A polynomial bound for the lap number ⋮ INVARIANCE OF KNEADING MATRIX UNDER CONJUGACY ⋮ One-Dimensional Semiconjugacy Revisited ⋮ The local Hölder exponent for the entropy of real unimodal maps ⋮ Computation of symbolic dynamics for one-dimensional maps

Cites Work

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• The universal metric properties of nonlinear transformations
• Piecewise invertible dynamical systems
• On intrinsic ergodicity of piecewise monotonic transformations with positive entropy
• On the abundance of aperiodic behaviour for maps on the interval
• On intrinsic ergodicity of piecewise monotonic transformations with positive entropy. II
• Bifurcations in one dimension. II. A versal model for bifurcations
• Iterates of piecewise monotone mappings on an interval
• The dynamics of density dependent population models
• On periodic points
• Zeta-functions and transfer-operators for piecewise linear transformations.
• Asymptotic behaviour of iterated piecewise monotone maps
• Periodic Orbits and Kneading Invariants
• The Periodic Orbits and Entropy of Certain Maps of the Unit Interval
• Entropy of piecewise monotone mappings
• The structure of piecewise monotonic transformations
• Deterministic Nonperiodic Flow
• Simple mathematical models with very complicated dynamics
• Symbolic Dynamics and Transformations of the Unit Interval

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