Transitivity and the centre for maps of the circle

DOI10.1017/S0143385700003254zbMath0607.58032MaRDI QIDQ3746551

Ethan M. Coven, Irene Mulvey

Publication date: 1986

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

transitivityperiodic pointsmaps of the circle

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Morse-Smale systems (37D15)

Related Items (29)

The centre and the depth of the centre for continuous maps on dendrites with finite branch points ⋮ Unnamed Item ⋮ Topological Conjugacy and Transitivity for a Class of Piecewise Monotone Maps of the Interval ⋮ Topological structure and entropy of mixing graph maps ⋮ Ergodic endomorphisms of compact Abelian groups ⋮ Supremum topological sequence entropy of circle maps ⋮ Topologically transitive and mixing properties of set-valued dynamical systems ⋮ Thermodynamical and spectral phase transition for local diffeomorphisms in the circle ⋮ Topological entropy of Devaney chaotic maps ⋮ Mixing properties in expanding Lorenz maps ⋮ The centre and the depth of the centre for continuous maps on dendrites with unique branch point ⋮ Linking and the Shadowing Property for Piecewise Monotone Maps ⋮ One-way intervals of circle maps ⋮ Non-wandering points and the depth for graph maps ⋮ Dense periodicity on graphs ⋮ Dynamics and indecomposable inverse limit spaces of maps on finite graphs ⋮ A Survey on the Relation Between Transitivity and Dense Periodicity for Graph Maps ⋮ Recurrent points and non-wandering points of graph maps ⋮ Exact Devaney chaos and entropy ⋮ On the topological entropy of transitive maps of the interval ⋮ The depths and the attracting centres for continuous maps on local dendrites with the number of branch points being finite ⋮ Transitivity and Dense Periodicity for Graph Maps ⋮ When lower entropy implies stronger Devaney chaos ⋮ Special \(\alpha \)-limit points and unilateral \(\gamma \)-limit points for graph maps ⋮ Circle maps and -algebras ⋮ The bifurcation set as a topological invariant for one-dimensional dynamics ⋮ Dynamics of quasicontinuous systems ⋮ The Role of Continuity and Expansiveness on Leo and Periodic Specification Properties ⋮ Devaney's chaotic on induced maps of hyperspace

Cites Work

• Continuous maps of the circle without periodic points
• Periodic Orbits of Continuous Mappings of the Circle
• Symbolic Dynamics and Transformations of the Unit Interval

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