Existence of blenders in a Hénon-like family: geometric insights from invariant manifold computations

DOI10.1088/1361-6544/aacd66zbMath1402.37027OpenAlexW2888434284MaRDI QIDQ4583366

Bernd Krauskopf, Stefanie Hittmeyer, Katsutoshi Shinohara, Hinke M. Osinga

Publication date: 28 August 2018

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1361-6544/aacd66

zbMATH Keywords

diffeomorphismnonuniform hyperbolicityblendersglobal invariant manifoldsHenon-like familythree-dimensional polynomial diffeomorphisms

Mathematics Subject Classification ID

Invariant manifold theory for dynamical systems (37D10) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Computational methods for bifurcation problems in dynamical systems (37M20) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items

FPGA REALIZATION OF COMPLEX LOGISTIC MAP FRACTAL BEHAVIOR, Determining the global manifold structure of a continuous-time heterodimensional cycle, How to identify a hyperbolic set as a blender, Blender-horseshoes in Center-unstable Hénon-like Families, Hénon-Like Families and Blender-Horseshoes at Nontransverse Heterodimensional Cycles

Uses Software

• DSTool

Cites Work

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• How to find a codimension-one heteroclinic cycle between two periodic orbits
• Shift automorphisms in the Henon mapping
• There are no \(C^{1}\)-stable intersections of regular Cantor sets
• On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors
• The dynamics of the Hénon map
• Pseudohyperbolicity and the problem on periodic perturbations of Lorenz-type attractors
• A two-dimensional mapping with a strange attractor
• Periodic orbits as the skeleton of classical and quantum chaos
• Growing 1D and quasi-2D unstable manifolds of maps
• Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective
• Persistent nonhyperbolic transitive diffeomorphisms
• Abundance of $C^{1}$-robust homoclinic tangencies
• Interacting Global Invariant Sets in a Planar Map Model of Wild Chaos
• Stabilization of heterodimensional cycles
• WHAT IS... a Blender?
• Homoclinic bifurcations that give rise to heterodimensional cycles near a saddle-focus equilibrium
• From wild Lorenz-like to wild Rovella-like dynamics
• An example of a wild strange attractor
• Computing Geodesic Level Sets on Global (Un)stable Manifolds of Vector Fields
• Deterministic Nonperiodic Flow
• Computing One-Dimensional Stable Manifolds and Stable Sets of Planar Maps without the Inverse
• Abundance of hyperbolicity in the $C^1$ topology
• Blenders in centre unstable Hénon-like families: with an application to heterodimensional bifurcations
• THREE-DIMENSIONAL HÉNON-LIKE MAPS AND WILD LORENZ-LIKE ATTRACTORS
• Shorter Notes: A 3-Dimensional Abraham-Smale Example