Persistent heterodimensional cycles in periodic perturbations of Lorenz-like attractors

DOI10.1088/1361-6544/ab5921zbMath1430.37028arXiv1712.02674OpenAlexW3000915039MaRDI QIDQ5212121

Dongchen Li, Dmitry V. Turaev

Publication date: 27 January 2020

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.02674

zbMATH Keywords

chaotic dynamicshomoclinic bifurcationLorenz attractorhomoclinic tangencyheterodimensional cycle

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Symmetries and invariants of dynamical systems (37C79)

Related Items (2)

Homoclinic tangencies leading to robust heterodimensional cycles ⋮ Scenarios for the creation of hyperchaotic attractors in 3D maps

Uses Software

• RODES

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Homoclinic tangencies to resonant saddles and discrete Lorenz attractors
• Existence of heterodimensional cycles near shilnikov loops in systems with a \(\mathbb{Z}_2\) symmetry
• On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors
• Invariants of \(\Omega\)-conjugacy of diffeomorphisms with a nongeneric homoclinic trajectory
• Pseudohyperbolicity and the problem on periodic perturbations of Lorenz-type attractors
• Bifurcations and stability of families of diffeomorphisms
• Method of quasinormal forms in the problem of steady-state conditions for parabolic systems with small diffusion
• Structural stability of Lorenz attractors
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
• Asymptotic normal for equilibria with a triplet of zero characteristic exponents in systems with symmetry
• High dimension diffeomorphisms displaying infinitely many periodic attractors
• A rigorous ODE solver and Smale's 14th problem
• Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers
• Persistent nonhyperbolic transitive diffeomorphisms
• Degenerate behavior in non-hyperbolic semigroup actions on the interval: fast growth of periodic points and universal dynamics
• Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model
• Homoclinic bifurcations that give rise to heterodimensional cycles near a saddle-focus equilibrium
• On dynamical properties of multidimensional diffeomorphisms from Newhouse regions: I
• ROBUST HETERODIMENSIONAL CYCLES AND $C^1$-GENERIC DYNAMICS
• Nonconnected heterodimensional cycles: bifurcation and stability
• Homoclinic Bifurcation to a Transitive Attractor of Lorenz Type, II
• The Lorenz attractor exists
• ON DIMENSION OF NON-LOCAL BIFURCATIONAL PROBLEMS
• NORMAL FORMS AND LORENZ ATTRACTORS
• Dynamical phenomena in systems with structurally unstable Poincaré homoclinic orbits
• Deterministic Nonperiodic Flow
• Computer assisted proof of the existence of the Lorenz attractor in the Shimizu–Morioka system
• Robust nonhyperbolic dynamics and heterodimensional cycles
• Persistence of cycles and nonhyperbolic dynamics at heteroclinic bifurcations
• C²-robust heterodimensional tangencies
• Expanding Lorenz Attractors through Resonant Double Homoclinic Loops
• ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. I
• Invariant manifolds

This page was built for publication: Persistent heterodimensional cycles in periodic perturbations of Lorenz-like attractors