Parameter-shifted shadowing property for geometric Lorenz attractors

DOI10.1090/S0002-9947-04-03607-4zbMath1073.37023arXivmath/0312161OpenAlexW1889115764MaRDI QIDQ3155961

Shin Kiriki, Teruhiko Soma

Publication date: 5 January 2005

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0312161

zbMATH Keywords

shadowing propertystrange attractorgeometric Lorenz model

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Complex behavior and chaotic systems of ordinary differential equations (34C28)

Related Items (6)

Specification and partial hyperbolicity for flows ⋮ Control of Julia sets of the complex Hénon system ⋮ On various types of shadowing for geometric Lorenz flows ⋮ Parameter-shifted shadowing property of Lozi maps ⋮ Unnamed Item ⋮ Oriented shadowing property and \(\Omega\)-stability for vector fields

Uses Software

• RODES

Cites Work

• Unnamed Item
• Lorenz attractors do not have the pseudo-orbit tracing property
• Is every approximate trajectory of some process near an exact trajectory of a nearby process?
• Structural stability of Lorenz attractors
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• Strange attractors across the boundary of hyperbolic systems
• A rigorous ODE solver and Smale's 14th problem
• Shadowing in dynamical systems
• Lorenz attractor through saddle-node bifurcations
• Maximal transitive sets with singularities for genericC 1 vector fields
• Mixing attractors for 3-flows
• Transverse surfaces and attractors for 3-flows
• Parameter-shifted shadowing property of Lozi maps
• Pseudo-Orbit Shadowing in the Family of Tent Maps
• Singular hyperbolic systems
• Deterministic Nonperiodic Flow
• What's new on Lorenz strange attractors?

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