Topological Conjugacy and Transitivity for a Class of Piecewise Monotone Maps of the Interval

DOI10.2307/2000600zbMath0614.54035OpenAlexW4240451861MaRDI QIDQ4721228

Ethan M. Coven, Louis Stuart Block

Publication date: 1987

Full work available at URL: https://doi.org/10.2307/2000600

zbMATH Keywords

topological conjugacytransitivityexpanding Markov mapslinear Markov mapsmaps of compact intervals

Mathematics Subject Classification ID

Related Items (32)

Dynamics of induced maps on the space of probability measures ⋮ Matrices induced by endomorphisms of finite sets ⋮ Invariant measures for maps of the interval that do not have points of some period ⋮ Period two implies chaos for a class of multivalued maps: a naive approach ⋮ Unnamed Item ⋮ The question on characteristic endpoints for iterative roots of PM functions ⋮ On the Ellis semigroup of a discrete dynamical system \(([0, 1, f)\)] ⋮ Dynamical properties of the shift maps on the inverse limit spaces ⋮ Conjugacy problem of strictly monotone maps with only one jump discontinuity ⋮ Induced dynamics of nonautonomous dynamical systems ⋮ Measure preserving interval maps and topological conjugacy ⋮ Topological entropy of Devaney chaotic maps ⋮ Shadowing, asymptotic shadowing and s-limit shadowing ⋮ Topological conjugacy, transitivity, and patterns ⋮ Typical properties of interval maps preserving the Lebesgue measure ^* ⋮ Shadowing, entropy and a homeomorphism of the pseudoarc ⋮ Forcing relation on patterns of invariant sets and reductions of interval maps ⋮ Linking and the Shadowing Property for Piecewise Monotone Maps ⋮ Topological conjugacy for multifunctions with finitely many set-valued points and an application to iterative roots ⋮ A topological classification for piecewise monotone iterative roots ⋮ Topological conjugacy between multifunctions ⋮ Topological conjugacy of PM functions with height equaling ∞ ⋮ Maps of the Interval with Every Point Chain Recurrent ⋮ Possible jumps of entropy for interval maps ⋮ On the topological entropy of transitive maps of the interval ⋮ A Complete Classification of the Piecewise Monotone Functions on the Interval ⋮ Variations on the concept of topological transitivity ⋮ The bifurcation set as a topological invariant for one-dimensional dynamics ⋮ A topological classification of interval mappings with finitely many discontinuous points ⋮ On the notion of random chaos ⋮ Brief survey on the topological entropy ⋮ Topological mixing, knot points and bounds of topological entropy

Cites Work

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• On a normal form of symmetric maps of \([0,1\)]
• Simple permutations with order a power of two
• Absolutely Continuous Invariant Measures that are Maximal
• Stratification of Continuous Maps of an Interval
• Transitivity and the centre for maps of the circle
• Entropy of piecewise monotone mappings
• On the Topology of the Set of Completely Unstable Flows
• Chaos, Periodicity, and Snakelike Continua
• Symbolic Dynamics and Transformations of the Unit Interval

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