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

• Published in: Nonlinearity Vol. 31; no. 12; pp. 5410 - 5440
• Main Authors: Capi ski, Maciej J, Turaev, Dmitry, Zgliczy ski, Piotr
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.12.2018
• Subjects: computer assisted proof; Lorenz attractor; Shimizu-Morioka system

We prove that the Shimizu-Morioka system has a Lorenz attractor for an open set of parameter values. For the proof we employ a criterion proposed by Shilnikov, which allows to conclude the existence of the attractor by examination of the behaviour of only one orbit. The needed properties of the orbi...