Computer assisted proof of the existence of the Lorenz attractor in the Shimizu–Morioka system

DOI10.1088/1361-6544/aae032zbMath1405.34048arXiv1711.10404OpenAlexW2770975716WikidataQ129020315 ScholiaQ129020315MaRDI QIDQ4644665

Maciej J. Capiński, Piotr Zgliczyński, Dmitry V. Turaev

Publication date: 8 January 2019

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.10404

zbMATH Keywords

Lorenz attractorShimizu-Morioka systemcomputer assisted proof

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Bifurcation theory for ordinary differential equations (34C23) Invariant manifold theory for dynamical systems (37D10) Complex behavior and chaotic systems of ordinary differential equations (34C28) Dynamical systems with hyperbolic orbits and sets (37D05) Attractors of solutions to ordinary differential equations (34D45) Dynamical aspects of attractors and their bifurcations (37G35) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (10)

On discrete homoclinic attractors of three-dimensional diffeomorphisms ⋮ On examples of pseudohyperbolic attractors in flows and maps ⋮ Validated Spectral Stability via Conjugate Points ⋮ On the birth of discrete Lorenz attractors under bifurcations of 3D maps with nontransversal heteroclinic cycles ⋮ Computer‐assisted analysis of chaos in a three‐species food chain model ⋮ Monotonicity and non-monotonicity regions of topological entropy for Lorenz-like families with infinite derivatives ⋮ Persistent heterodimensional cycles in periodic perturbations of Lorenz-like attractors ⋮ Wild pseudohyperbolic attractor in a four-dimensional Lorenz system ⋮ Lorenz attractors and the modular surface ^* ⋮ On discrete Lorenz-like attractors

Uses Software

• RODES

Cites Work

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