Constructing complete chaotic maps with reciprocal structures. (English) Zbl 1134.37336

Huang, Weihong

Discrete Dyn. Nat. Soc. 2005, No. 3, 357-372 (2005).

Summary: A class of unimodal complete chaotic maps \(f=\{f_{L},f_{R}\}\) with reciprocal functional forms \((f_{R}=1/f_{L})\) are examined. The necessary and sufficient conditions are provided to construct such maps. The theoretical conclusions are then verified by numerical simulations.

MSC:

37E05	Dynamical systems involving maps of the interval
37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37A05	Dynamical aspects of measure-preserving transformations
37B99	Topological dynamics

Keywords:

chaos; Lyapunov exponents; interval map; invariant measures; unimodal maps