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RESEARCH PRODUCT

Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations

Nikolay KuznetsovNikolay KuznetsovGennady A. LeonovT.a. Alexeeva

subject

Lyapunov functionMathematics::Dynamical SystemsComputationFOS: Physical sciencesAerospace EngineeringOcean EngineeringDynamical Systems (math.DS)Lyapunov exponent01 natural sciencessymbols.namesakeExponential growthComputer Science::Systems and Control0103 physical sciencesFOS: MathematicsApplied mathematics0101 mathematicsElectrical and Electronic EngineeringMathematics - Dynamical Systems010301 acousticsMathematicsApplied MathematicsMechanical Engineering010102 general mathematicsNonlinear Sciences - Chaotic DynamicsNonlinear Sciences::Chaotic DynamicsSingular valueFundamental matrix (linear differential equation)Control and Systems EngineeringsymbolsDiffeomorphismChaotic Dynamics (nlin.CD)Characteristic exponent

description

Nowadays the Lyapunov exponents and Lyapunov dimension have become so widespread and common that they are often used without references to the rigorous definitions or pioneering works. It may lead to a confusion since there are at least two well-known definitions, which are used in computations: the upper bounds of the exponential growth rate of the norms of linearized system solutions (Lyapunov characteristic exponents, LCEs) and the upper bounds of the exponential growth rate of the singular values of the fundamental matrix of linearized system (Lyapunov exponents, LEs). In this work the relation between Lyapunov exponents and Lyapunov characteristic exponents is discussed. The invariance of Lyapunov exponents for regular and irregular linearizations under the change of coordinates is demonstrated.

yearjournalcountryeditionlanguage
2014-10-08
10.1007/s11071-016-2678-4http://arxiv.org/abs/1410.2016