User:James Meiss/Proposed/Henon map

• Michael Benedicks, Department of Mathematics, KTH, Stockholm, Sweden

Dr. Michael Benedicks accepted the invitation on 2 July 2007 (self-imposed deadline: 2 September 2007).

This article will briefly cover: (preliminarily)

Hénon's computer experiment and the phenemenology. (Relation to Lorenz system.) Concept of attractor(cf. Milnor's article). The idea of positive Lyapunov exponent and the Collet-Eckmann condition (positive Lyapunov exponent on the critical orbit(s)). Parameter choices (Cantor sets of positive measure). The concept of a critical set for Hénon maps. The ideas of invariant measures, SRB-measures, positive entropy (Sinai's and Katok's contributions). Relation between Lyapunov exponents and entropy and dimension. Statistical behaviour and correlation.