A Cr unimodal map with an arbitrary fast growth of the number of periodic points

DOI10.1017/S0143385710000817zbMath1247.37034MaRDI QIDQ2884079

O. S. Kozlovski, Vadim Yu. Kaloshin

Publication date: 24 May 2012

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

neutral periodic pointsuperexponential growthinfinitely renormalizable map

Mathematics Subject Classification ID

Orbit growth in dynamical systems (37C35) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Dynamical systems involving maps of the interval (37E05)

Related Items (7)

Abundance of fast growth of the number of periodic points in two-dimensional area-preserving dynamics ⋮ Growth of number of periodic orbits of one family of skew product maps ⋮ On the structure of isentropes of polynomial maps ⋮ A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I ⋮ Fast growth of the number of periodic points arising from heterodimensional connections ⋮ The Many Facets of Chaos ⋮ Periodic attractors of perturbed one-dimensional maps

Cites Work

• Generic 3-dimensional volume-preserving diffeomorphisms with superexponential growth of number of periodic orbits
• Julia-Fatou-Sullivan theory for real one-dimensional dynamics
• The periodic points of renormalization
• On models with non-rough Poincaré homoclinic curves
• Generic diffeomorphisms with superexponential growth of number of periodic orbits
• An extension of the Artin-Mazur theorem
• On periodic points
• A computer-assisted proof of the Feigenbaum conjectures

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