A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I

DOI10.1090/S1079-6762-01-00090-7zbMath0977.37007MaRDI QIDQ2761163

Brian R. Hunt, Vadim Yu. Kaloshin

Publication date: 17 December 2001

Published in: Electronic Research Announcements of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/224424

zbMATH Keywords

prevalencediffeomorphismsperiodic points

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Periodic orbits of vector fields and flows (37C27) Orbit growth in dynamical systems (37C35) Generic properties, structural stability of dynamical systems (37C20) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27)

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Cites Work

• Julia-Fatou-Sullivan theory for real one-dimensional dynamics
• On models with non-rough Poincaré homoclinic curves
• Generic diffeomorphisms with superexponential growth of number of periodic orbits
• On the entropy of holomorphic maps
• An extension of the Artin-Mazur theorem
• On periodic points
• A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II
• A C^r unimodal map with an arbitrary fast growth of the number of periodic points
• A quantitative version of the Kupka-Smale theorem
• Prevalence: a translation-invariant “almost every” on infinite-dimensional spaces
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