Analytic Lyapunov exponents in a classical nonlinear field equation

Anno: 2000

Autori: Franzosi R., Gatto R., Pettini G., Pettini M.

Affiliazione autori: Dipartimento di Fisica dell’Università, Largo Enrico Fermi 2, 50125 Firenze, Italy; Departement de Physique Théorique, Université de Genève, 24 Quai Ernest-Ansermet, CH-1211 Geneve, Switzerland; Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, 50125 Firenze, Italy

Abstract: It is shown that the nonlinear wave equation partial derivative(t)(2)phi-partial derivative(x)(2)phi-mu(0)partial derivative(x)(partial derivative(x)phi)(3)=0, which is the continuum limit of the Fermi-Pasta-Ulam beta model, has a positive Lyapunov exponent lambda(1), whose analytic energy dependence is given. The result (a first example for field equations) is achieved by evaluating the lattice-spacing dependence of lambda(1) for the FPU model within the framework of a Riemannian description of Hamiltonian chaos. We also discuss a difficulty of the statistical mechanical treatment of this classical field system, which is absent in the dynamical description.

Giornale/Rivista: PHYSICAL REVIEW E

Volume: 61 (4)      Da Pagina: R3299  A: R3302

Parole chiavi: Differential equations; Lyapunov functions; Lyapunov methods; Nonlinear equations, Continuum limits; Energy dependence; Hamiltonian chaos; Lyapunov exponent; Nonlinear field equations; Nonlinear wave equation; Spacing dependence; Statistical mechanical treatment, Hamiltonians
DOI: 10.1103/PhysRevE.61.R3299

Citazioni: 3
dati da “WEB OF SCIENCE” (of Thomson Reuters) aggiornati al: 2025-05-18
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