Characterizing Dynamics with Covariant Lyapunov Vectors

2007/06/04 by F. Ginelli, Francesco Ginelli, Pablo M. Poggi +9 · 5 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Basis (linear algebra) #Covariant transformation #Dynamical systems theory #Geometry #Lyapunov equation #Lyapunov exponent #Lyapunov function #Mathematical physics #Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Physics #Pure mathematics #Quantum chaos and dynamical systems #Quantum mechanics #Statistical physics #Transversality #cond-mat.stat-mech #nlin.CD

paper · pdf · doi:10.1103/physrevlett.99.130601

published as Phys Rev Lett 99, 130601 (2007). · 4 pages, 3 figures, submitted to Physical Review letters

arxiv created 2007/06/04 · openalex publication_date 2007/09/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A general method to determine covariant Lyapunov vectors in both discrete- and continuous-time dynamical systems is introduced. This allows us to address fundamental questions such as the degree of hyperbolicity, which can be quantified in terms of the transversality of these intrinsic vectors. For spatially extended systems, the covariant Lyapunov vectors have localization properties and spatial Fourier spectra qualitatively different from those composing the orthonormalized basis obtained in the standard procedure used to calculate the Lyapunov exponents.

Citations

• From synchronization to Lyapunov exponents and back
• CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems

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Related

• Theory and computation of covariant Lyapunov vectors
• Covariant Lyapunov vectors as global solutions of a partial differential equation on the phase space
• Localization Properties of Covariant Lyapunov Vectors
• Symmetry properties of orthogonal and covariant Lyapunov vectors and their exponents
• Structure of characteristic Lyapunov vectors in spatiotemporal chaos