The Dynamics of Continuous Maps of Finite Graphs through Inverse Limits

DOI10.2307/2154506zbMath0812.58024OpenAlexW4240843245MaRDI QIDQ4311351

Beverly Diamond, Marcy M. Barge

Publication date: 26 October 1994

Full work available at URL: https://doi.org/10.2307/2154506

zbMATH Keywords

horseshoeperiodic orbitscontinuous mapstopological entropyfinite graphinverse limit space

Mathematics Subject Classification ID

Entropy in general topology (54C70) Low-dimensional dynamical systems (37E99)

Related Items (22)

New chaotic planar attractors from smooth zero entropy interval maps ⋮ Entropy, periodicity, and graphs with zero Euler characteristic ⋮ Homoclinic points and topological entropy of a continuous mapping of a dendrite ⋮ Chaos and indecomposability ⋮ The topology and dynamics of the hyperspaces of normal fuzzy sets and their inverse limit spaces ⋮ On entropy of graph maps that give hereditarily indecomposable inverse limits ⋮ The Mean Sensitivity and Mean Equicontinuity in Uniform Spaces ⋮ \(\mathcal{F}\)-mixing property and \((\mathcal{F}_1,\mathcal{F}_2)\)-everywhere chaos of inverse limit dynamical systems ⋮ Hereditarily indecomposable inverse limits of graphs: shadowing, mixing and exactness ⋮ The inverse limits approach to chaos ⋮ On piecewise-monotone mappings with closed set of periodic points on dendrites ⋮ Chaos in the sense of Li-Yorke and the order of the inverse limit space. ⋮ Topological entropy and IE-tuples of indecomposable continua ⋮ Backward dynamics in economics. The inverse limit approach ⋮ A classification of inverse limit spaces of tent maps with a nonrecurrent critical point ⋮ Chaotic continua in chaotic dynamical systems ⋮ Monotone maps of 𝐺-like continua with positive topological entropy yield indecomposability ⋮ Shadowing for induced maps of hyperspaces ⋮ Adding machines and endpoints ⋮ Generalized horseshoes and indecomposability for one-dimensional continua ⋮ On inverse limit spaces of maps of an interval with zero entropy ⋮ On homeomorphisms of \((I,f)\) having topological entropy zero

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Monotone decompositions of inverse limit spaces based on finite graphs
• Circle maps and inverse limits
• The pseudo-arc as an inverse limit with one binding map
• One-dimensional non-wandering sets
• The Construction of Global Attractors
• Irreducibility and indecomposability in inverse limits
• Chaos, Periodicity, and Snakelike Continua
• Topological Entropy
• Entropy for Group Endomorphisms and Homogeneous Spaces

This page was built for publication: The Dynamics of Continuous Maps of Finite Graphs through Inverse Limits