Analysis of spurious synchronization with positive conditional Lyapunov exponents in computer simulations
type: Item
instance of: scholarly article
title: Analysis of spurious synchronization with positive conditional Lyapunov exponents in computer simulations
zbMATH Open document ID: 0997.37060
DOI: 10.1016/S0167-2789(99)00127-X
author: Yanyan Li
published in: Physica D
publication date: 2002-11-19T00:00:00Z
review text: This paper deals with partially hyperbolic diffeomorphisms preserving a splitting of the tangent bundle into a strong-unstable subbundle \(E^{\text{un}}\) (uniformly expanding) and a subbundle \(E^c\), dominated by \(E^{\text{un}}\). They show that if the central direction \(E^c\) is mostly contracting for the diffeomorphism, then the ergodic Gibbs \(u\)-states are the SRB measures, there are finitely many of them, and their basins cover a full measure subset. Moreover, they prove that if the strong-unstable leaves are dense, then there is a unique SRB measure. The authors also provide some applications of the results mentioned above.
Mathematics Subject Classification ID: 37M05
Mathematics Subject Classification ID: 37A30
zbMATH DE Number: 1394434
zbMATH Keywords: synchronization
zbMATH Keywords: Lyapunov exponent
zbMATH Keywords: unstable subbundle
zbMATH Keywords: partially hyperbolic diffeomorphisms
zbMATH Keywords: ergodic Gibbs \(u\)-states
zbMATH Keywords: SRB measures
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Synchronization in chaotic systems
cites work: Transition to chaos for random dynamical systems
cites work: Invariant Manifolds and Synchronization of Coupled Dynamical Systems
cites work: Controlling chaos
full work available at URL: s0167-2789(99)00127-x
OpenAlex ID: W2060405447
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description: scientific article; zbMATH DE number 1394434