Periodic and Limit Orbits and the Depth of the Center for Piecewise Monotone Interval Maps

DOI10.2307/2043751zbMath0478.58019OpenAlexW4245133041MaRDI QIDQ3935902

Zbigniew H. Nitecki

Publication date: 1980

Full work available at URL: https://doi.org/10.2307/2043751

zbMATH Keywords

nonwandering setBirkhoff centerdepth of the center for piecewise monotone interval mapsiterated self maps of the intervalperiodic and limit orbits

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (12)

A 𝐶¹ function for which the 𝜔-limit points are not contained in the closure of the periodic points ⋮ Continuity of the maps \(f\mapsto\bigcup_{x\in I}\omega(x,f)\) and \(f\mapsto\{\omega(x,f):x\in I\}\) ⋮ The centre and the depth of the centre for continuous maps on dendrites with unique branch point ⋮ Relations Between Chain Recurrent Points and Turning Points on the Interval ⋮ Recurrent points and non-wandering points of graph maps ⋮ Functional Rotation Numbers for One-Dimensional Maps ⋮ ω-limit sets for maps of the interval ⋮ Structures of quasi-graphs and $\omega $-limit sets of quasi-graph maps ⋮ Special \(\alpha \)-limit points and unilateral \(\gamma \)-limit points for graph maps ⋮ Recurrent and periodic points in dendritic Julia sets ⋮ Non-wandering sets of the powers of maps of the interval ⋮ Topological structure of non-wandering set of a graph map

Cites Work

• A closing lemma on the interval
• Flows on nonorientable 2-manifolds
• _ P   = _ R   for Maps of the Interval
• Diffeomorphisms Obtained from Endomorphisms
• Central Sequences in Flows on 2-Manifolds of Finite Genus
• Central Sequences in Dynamical Systems

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