Eur. Phys. J. B 46, 409-417 (2005)
https://doi.org/10.1140/epjb/e2005-00269-1

Anomalous sensitivity to initial conditions and entropy production in standard maps: Nonextensive approach

¹ Departamento Académico de Física, Universidad Nacional de Trujillo, Av. Juan Pablo II, s/n, Trujillo, Peru
² Universidad de Guadalajara, Campus Universitario Los Lagos Av. Enrrique Diaz de Leon s/n, Fracc. Paseo de la Montaña. C.P. 47460 Lagos de Moreno, Jal., Mexico
³ INFM-Dipartimento di Fisica, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
⁴ Sezione INFN, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
⁵ Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA
⁶ Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil

Corresponding authors: ^a fedorja@cbpf.br - ^b baldovin@pd.infn.it - ^c tsallis@cbpf.br

Received: 2 March 2005
Published online: 18 August 2005

Abstract

We perform a throughout numerical study of the average sensitivity to initial conditions and entropy production for two symplectically coupled standard maps focusing on the control-parameter region close to regularity. Although the system is ultimately strongly chaotic (positive Lyapunov exponents), it first stays lengthily in weak-chaotic regions (zero Lyapunov exponents). We argue that the nonextensive generalization of the classical formalism is an adequate tool in order to get nontrivial information about the first stage of this crossover phenomenon. Within this context we analyze the relation between the power-law sensitivity to initial conditions and the entropy production.