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

Abstract

We prove, by employing rigorous numerics, that Shimizu-Morioka system has a Lorenz attractor for an open set of parameter values. Using this result, we prove the existence of a discrete version of the Lorenz attractor for a class of three-dimensional polynomial diffeomorphisms.

References in corpus (4)

• Chaotic dynamics of three-dimensional Hénon maps that originate from a homoclinic bifurcation
• Birth of discrete Lorenz attractors at the bifurcations of 3D maps with homoclinic tangencies to saddle points
• Persistent heterodimensional cycles in periodic perturbations of Lorenz-like attractors
• On birth of discrete Lorenz attractors under bifurcations of 3D maps with nontransversal heteroclinic cycles

Cited by in corpus (3)

• Lorenz attractors and the modular surface
• On Hyperbolic Attractors in Complex Shimizu -- Morioka Model
• Persistent heterodimensional cycles in periodic perturbations of Lorenz-like attractors