Randomization of Sharkovskii-type theorems

DOI10.1090/S0002-9939-07-09242-8zbMath1132.37016OpenAlexW2061421853MaRDI QIDQ5441179

Jan Andres

Publication date: 8 February 2008

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-07-09242-8

zbMATH Keywords

randomizationtransversal mapsrandom periodic orbitstransformation to deterministic caserandom generalizationsSharkovskij-type theorems

Mathematics Subject Classification ID

Set-valued operators (47H04) Generation, random and stochastic difference and differential equations (37H10) Dynamical systems involving maps of the interval (37E05) Combinatorial dynamics (types of periodic orbits) (37E15) Random nonlinear operators (47H40)

Related Items (11)

Recent results on the topological fixed point theory of multivalued mappings: a survey ⋮ A Multivalued Version of the Block–Sharkovsky Theorem Applicable to Differential Equations on the Circle ⋮ Randomization of Sharkovsky-type results on the circle ⋮ Sharkovsky-Type Theorems on S1 Applicable to Differential Equations ⋮ The Sharkovskiĭ Theorem for spaces of measurable functions ⋮ Randomized Sharkovsky-type results and random subharmonic solutions of differential inclusions ⋮ Sharp Block–Sharkovsky Type Theorem for Multivalued Maps on the Circle and Its Application to Differential Equations and Inclusions ⋮ Continuous functions in rings generated by a single Darboux function ⋮ Randomized Sharkovsky-type theorems and their application to random impulsive differential equations and inclusions on tori ⋮ Application of the randomized Sharkovsky-type theorems to random impulsive differential equations and inclusions ⋮ On the notion of random chaos

Cites Work

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• Sharkovskii's theorem, differential inclusions, and beyond
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• COEXISTENCE OF CYCLES OF A CONTINUOUS MAP OF THE LINE INTO ITSELF
• PERIODICITY AND SHARKOVSKY'S THEOREM FOR RANDOM DYNAMICAL SYSTEMS
• Sharkovskiĭ's theorem holds for some discontinuous functions
• A version of Sharkovskii’s theorem for differential equations
• Period two implies all periods for a class of ODEs: A multivalued map approach
• LOW-DIMENSIONAL COMBINATORIAL DYNAMICS
• Topological Fixed Point Theory of Multivalued Mappings

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