EVENT DETAILS AND ABSTRACT

Title: Kneading theory for 2-dimensional maps: the pruning front conjecture
Speaker: Professor Predrag Cvitanovic'
Speaker Info: Northwestern, Department of Physics & Astronomy
Brief Description:
Special Note:
Abstract:

We construct a 2-d representation of the symbolic dynamics for maps of the Henon type. This is a ``road map" in which the various sheets of the stable and unstable manifolds are represented by straight sections, and the topology is preserved: the nearby periodic points in the symbol plane represent nearby periodic points in the phase space. Next we separate the admissible and the forbidden orbits by means of a ``pruning front", a boundary between the two kinds of orbits. We make following assumptions:

1 The partition conjecture (Grassberger-Kantz): The non-wandering set of a map of the Henon type can be described by a subset of a complete Smale horseshoe, partitioned by the set of primary turning points.

2 The pruning-front conjecture (Cvitanovic-Gunaratne-Procaccia): Kneading values of the set of all primary turning points separate the admissible from the forbidden orbits, and there are no other pruning rules.

3 Multimodal map approximation (KT Hansen): A 2-dimensional map of the Henon type can be systematically approximated by a sequence of 1-dimensional n-folding maps.

The talk is heuristic and motivational; parts of the program have been put on firm footing by A. de Carvalho and Y. Ishii.