6533b85cfe1ef96bd12bcc07

RESEARCH PRODUCT

The Lyapunov dimension formula for the global attractor of the Lorenz system

N. A. KorzhemanovaGennady A. LeonovNikolay KuznetsovNikolay KuznetsovD. V. Kusakin

subject

Lyapunov functionClass (set theory)Mathematics::Dynamical SystemsKaplan-Yorke dimensionFOS: Physical sciencesLyapunov exponentDynamical Systems (math.DS)01 natural sciencesMeasure (mathematics)010305 fluids & plasmassymbols.namesakeDimension (vector space)Lorenz system0103 physical sciencesAttractorFOS: MathematicsMathematics - Dynamical Systems010301 acousticsMathematicsNumerical AnalysisApplied MathematicsMathematical analysista111Lyapunov exponentsLorenz systemNonlinear Sciences - Chaotic DynamicsNonlinear Sciences::Chaotic DynamicsModeling and SimulationsymbolsLyapunov dimensionself-excited Lorenz attractorVariety (universal algebra)Chaotic Dynamics (nlin.CD)

description

The exact Lyapunov dimension formula for the Lorenz system has been analytically obtained first due to G.A.Leonov in 2002 under certain restrictions on parameters, permitting classical values. He used the construction technique of special Lyapunov-type functions developed by him in 1991 year. Later it was shown that the consideration of larger class of Lyapunov-type functions permits proving the validity of this formula for all parameters of the system such that all the equilibria of the system are hyperbolically unstable. In the present work it is proved the validity of the formula for Lyapunov dimension for a wider variety of parameters values, which include all parameters satisfying the classical physical limitations. One of the motivation of this work is the possibility of computing a chaotic attractor in the Lorenz system in the case of one unstable and two stable equilibria.

yearjournalcountryeditionlanguage
2015-08-29
https://dx.doi.org/10.48550/arxiv.1508.07498