Coexistence phenomena in the Hénon family

DOI10.1007/s00574-023-00345-9zbMath1525.37041arXiv1811.00517OpenAlexW2898770886MaRDI QIDQ6116431

Michael Benedicks, Liviana Palmisano

Publication date: 11 August 2023

Published in: Bulletin of the Brazilian Mathematical Society. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.00517

zbMATH Keywords

attractorsHénon maps

Mathematics Subject Classification ID

Periodic orbits of vector fields and flows (37C27) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Stability theory for difference equations (39A30) Bifurcation theory for difference equations (39A28)

Cites Work

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• On the Henon transformation
• The dynamics of the Hénon map
• Bifurcation to infinitely many sinks
• A two-dimensional mapping with a strange attractor
• On iterations of \(1-\alpha x^2\) on \((-1,1)\)
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
• Abundance of strange attractors
• Sinai-Bowen-Ruelle measures for certain Hénon maps
• Diffeomorphisms with infinitely many sinks
• Toward a theory of rank one attractors
• Unfolding of chaotic unimodal maps and the parameter dependence of natural measures
• On dynamical properties of multidimensional diffeomorphisms from Newhouse regions: I
• On the approximation of Hénon-like attractors by homoclinic tangencies
• Solution of the basin problem for Hénon-like attractors
• Strange attractors with one direction of instability

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