On a multivalued version of the Sharkovskii theorem and its application to differential inclusions

DOI10.1023/A:1014488216807zbMath1082.37048MaRDI QIDQ1602974

Jan Andres, Libor Jüttner, Jiří Fišer

Publication date: 24 June 2002

Published in: Set-Valued Analysis (Search for Journal in Brave)

zbMATH Keywords

differential inclusionsperiodic orbitssubharmonicsmultiplicity resultsSharkovskii theoremLi-Yorke theoremmulti-valued version

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Ordinary differential inclusions (34A60) Low-dimensional dynamical systems (37E99) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (11)

Periods 1 + 2 imply chaos in steep or nonsmooth maps ⋮ Period two implies all periods for a class of ODEs: A multivalued map approach ⋮ Stability of periodic orbits and return trajectories of continuous multi-valued maps on intervals ⋮ A version of Sharkovskii’s theorem for differential equations ⋮ The hidden unstable orbits of maps with gaps ⋮ Full analogy of Sharkovsky's theorem for lower semicontinuous maps ⋮ SHARKOVSKII'S THEOREM FOR CONNECTIVITY G_δ-RELATIONS ⋮ On a multivalued version of the Sharkovskii theorem and its application to differential inclusions. II ⋮ Period three plays a negative role in a multivalued version of Sharkovskii's theorem ⋮ Period two implies chaos for a class of ODEs ⋮ Periodic points of multivalued mappings with applications to differential inclusions on tori.

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