Keller G (1996)
Publication Type: Book chapter / Article in edited volumes
Publication year: 1996
Publisher: North-Holland, Amsterdam
Edited Volumes: Stochastic and spatial structures of dynamical systems (Amsterdam, 1995)
Series: Konink. Nederl. Akad. Wetensch. Verh. Afd. Natuurk. Eerste Reeks, 45
Pages Range: 71--80
We describe the transfer operator approach to coupled map lattices (CML) in cases where the local map is expanding but has no Markov partition (e.g. a general tent map). The coupling is allowed to be non-local, but the total influence of all sites j<F NaN> 6= i on site i must be small. The main technical tool are lattice-size independent estimates of Lasota-Yorke type which show that the transfer (Perron-Frobenius) operator of the coupled system is quasicompact as an operator on the space of functions of bounded variation. 1 Introduction The purpose of this note is to summarize results from [11] and from the unpublished thesis [12]. Let L be a finite or countable index set, e.g. L = Zor L = Zn dZ. We investigate time-discrete dynamics on the state space X = [0; 1] L that are composed of independent chaotic actions on each component [0; 1] of X followed by some weak interaction that does not destroy the chaotic character of the whole system. More specifically, let ø : [0; 1] ! [0; 1]...
APA:
Keller, G. (1996). Coupled map lattice via transfer operators on functions of bounded variation. In S.J. van Strien, S.M. Verduyn Lunel (Eds.), Stochastic and spatial structures of dynamical systems (Amsterdam, 1995). (pp. 71--80). North-Holland, Amsterdam.
MLA:
Keller, Gerhard. "Coupled map lattice via transfer operators on functions of bounded variation." Stochastic and spatial structures of dynamical systems (Amsterdam, 1995). Ed. S.J. van Strien, S.M. Verduyn Lunel, North-Holland, Amsterdam, 1996. 71--80.
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