An Interdisciplinary Journal

* 2008, Vol.11, No.2, pp.233-240*

A one-dimensional chain of weakly coupled symplectic maps is
studied. We examine the existence and the size of the stability
regions around specific periodic orbits in the phase space of the
system with respect to the length of the chain and the coupling
strength between the oscillators. In order to accomplish this, we
consider a set of orbits defined by a grid of initial conditions
in a proper section of the phase space of the system and classify
them according to their regularity using the fast Lyapunov
indicator (FLI) as a chaos indicator. The correlation between the
existence of stability islands and the linear stability of the
corresponding periodic orbits is demonstrated. The results of our
study are used in order to examine the stability properties of
Discrete Breathers (DBs) i.e. spatially localized oscillations in
extended systems. Finally, we illustrate how this method can be
used in order to indicate the existence of DBs and other
breather-like motions.

*Key words: *
breather-like motion, coupled symplectic maps, Lyapunov
indicator

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Last updated: *July 10, 2008*