Stable synchronised states of coupled Tchebyscheff maps

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10 Citations (Scopus)


Coupled Tchebyscheff maps have recently been introduced to explain parameters in the standard model of particle physics, using the stochastic quantisation of Parisi and Wu. This paper studies dynamical properties of these maps, finding analytic expressions for a number of periodic states and determining their linear stability. Numerical evidence is given for nonlinear stability of some of these states, and also the presence of exponentially slow dynamics for some ranges of the parameter. These results indicate that a theory of particle physics based on coupled map lattices must specify strong physical arguments for any choice of initial conditions, and explain how stochastic quantisation is obtained in the many stable parameter regions.
Translated title of the contributionStable synchronised states of coupled Tchebyscheff maps
Original languageEnglish
Pages (from-to)88 - 102
Number of pages15
JournalPhysica D: Nonlinear Phenomena
Volume172 (1-4)
Publication statusPublished - Nov 2002

Bibliographical note

Publisher: Elsevier B.V

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