Isolating blocks and symbolic dynamics

Sturm's algorithm and isolating blocks

A topological existence proof for certain solutions of the Newtonian three-body problem is based on the construction of isolating blocks for the flow on an integral manifold. An isolating block is a submanifold whose boundary satisfies a convexity condition with respect to the three-body flow. Verifying this convexity condition can be reduced to the problem of checking the sign of a very compli...

Complex Dynamics and Symbolic Dynamics

Robert L. Devaney, Boston University Synopsis As so often happens in mathematics, there is a surprising connection between two quite distinct subfields of dynamical systems theory, namely the structure of the automorphism group of the one sided shift map on d-symbols and the topology of the analogue of the Mandelbrot set for degree d polynomials of one complex variable. In this lecture we will ...

Symbolic dynamics and representations

The object of study of symbolic dynamics are discrete dynamical systems made of infinite sequences of symbols, with the shift acting on them. They come as codings of trajectories of points in a dynamical system according to a given partition. They are used as discretization tools for analyzing such trajectories, but they also occur in a natural way in arithmetics for instance. We first will rec...

Symbolic Dynamics and Finite

Symbolic dynamics

This chapter presents some of the links between automata theory and symbolic dynamics. The emphasis is on two particular points. The first one is the interplay between some particular classes of automata, such as local automata and results on embeddings of shifts of finite type. The second one is the connection between syntactic semigroups and the classification of sofic shifts up to conjugacy.