Topics in numerical linear algebra and discrete dynamical systems
00-072 Wolf-Jürgen Beyn.
A Note on Symbolic Dynamics near Connecting Orbits of
Maps
In this note we consider the dynamics
of a diffeomorphism on a maximal, invariant set in the
neighborhood of a transversal homoclinic orbit. It is shown
that the map conjugates to a topological Markov chain on a
finite number of symbols defined by a special transition
matrix. The theorem collects in a unified way various
well-known results of Smale, Shilnikov,Palmer and others on
symbolic dynamics. Generalizations of the result are indicated
for finite sets of hyperbolic fixed points with a given finite
collection of transversal connecting orbits between
them.
