Complete description of weakly coupled chaotic subsystems
Lev Glebsky1 and Antonio Morante2
Instituto de Investigación en Comunicación Óptica, UASLP Av. Karakorum # 1470, Lomas 4ta sección, San Luis Potosí, SLP México. 1 glebsky@cactus.iico.uaslp.mx 2 amorante@cactus.iico.uaslp.mx
Recibido el 25 de agosto de 2000. ]]> Aceptado el 3 de junio de 2002.
Abstract
We study the dynamics of one-dimensional lattices of weakly coupled maps of R. The local dynamics has an invariant hyperbolic set. Moreover, the trajectories from non expanding (and weakly expanding) points go to infinity (for local dynamical system). Under these assumptions we show that, if the coupling is weak enough, the extended system has similar dynamics.
Keywords: Coupled map lattices, chaos, partial differential equations.
Resumen
Estudiamos la dinámica de enrejados unidimensionales de mapeos de R. acoplados débilmente. La dinámica local tiene un conjunto hiperbólico invariante. Además, las trayectorias de puntos no expansivos (y débilmente expansivos) van a infinito (para el sistema dinámico local). Bajo estos supuestos mostramos que, si el acoplamiento es suficientemente débil, el sistema extendido tiene una dinámica similar.
Descriptores: Enrejados de mapeos acoplados, caos, ecuaciones diferenciales.
]]> PACS: 05.45.Pq; 05.45.Jn
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Acknowledgements
This paper was written while L.G. was visiting IICO-UASLP. He thanks CONACYT, Universidad Autónoma de San Luis Potosí and IICO for their hospitality and support of this work. A. M. is a CONACYT fellow No. 128036 at IICO-UASLP and participant in the project M99-P01 of ANUIES-ECOS/Nord. The authors also thank professor V. Afraimovich for useful discussions.
References
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