Periodic segment implies infinitely many periodic solutions

DOI10.1090/S0002-9939-07-08750-3zbMath1139.37011OpenAlexW2041754639MaRDI QIDQ3438131

Klaudiusz Wójcik, Wacław Marzantowicz

Publication date: 15 May 2007

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-07-08750-3

zbMATH Keywords

periodic solutionfixed point indexsymbolic dynamicsLefschetz numberPoincaré map

Mathematics Subject Classification ID

Related Items (3)

Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers ⋮ Chaotic dynamics via index maps ⋮ Dold sequences, periodic points, and dynamics

Cites Work

• A geometric method for detecting chaotic dynamics
• Fixed point indices of iterated maps
• A remark on the Lefschetz fixed point formula for differentiable maps
• Combinatorial identities in dual sequences
• Finding periodic points of a map by use of a \(k\)-adic expansion
• Periodic and bounded solutions in blocks for time-periodic nonautonomous ordinary differential equations
• On detecting periodic solutions and chaos in the time periodically forced ODEs
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