Types d'orbites et dynamique minimale pour les applicationes continues de graphes

We define the type of a periodic orbit of a graph map. We consider the class of ‘train-track’ representatives, that is, those graph maps which minimize the topological entropy of the topological representatives of a given free group endomorphism. We prove that each type of periodic orbit realized by an efficient representative is also realised by any representative of the same free group endomorphism. Moreover, the number of periodic orbits of a given type is minimized by the efficient representatives

A note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits

The real-collapse Initial segments of models of arithmetic and the construction of the reals

SIGLEAvailable from British Library Document Supply Centre- DSC:DX181773 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

A note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits

A note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits

Stable heteroclinic cycles and symbolic dynamics

Let S 1 0, S 1 1,...,S 1 n−1 be n circles. A rotation in n circles is a map f:∪ i=0 n−1 S 1 i →∪ i=0 n−1 S 1 i which maps each circle onto another by a rotation. This particular type of interval exchange map arises naturally in bifurcation theory. In this paper we give a full description of the symbolic dynamics associated to such maps

Types d'orbites et dynamique minimale pour les applicationes continues de graphes

We define the type of a periodic orbit of a graph map. We consider the class of ‘train-track’ representatives, that is, those graph maps which minimize the topological entropy of the topological representatives of a given free group endomorphism. We prove that each type of periodic orbit realized by an efficient representative is also realised by any representative of the same free group endomorphism. Moreover, the number of periodic orbits of a given type is minimized by the efficient representatives