Chaotic Properties of Mappings on a Probability Space

By Christophe Abraham, Gérard Biau, Benoît Cadre. 2002

57 citations recorded by the source corpus.

Sensitive dependence on initial conditions is widely understood as being the central idea of chaos. We first give sufficient conditions (both topological and ergodic) on an endomorphism to ensure the sensitivity property. Then, a strong sensitivity concept is introduced. Sufficient conditions on a transformation implying strong sensitivity are given. We also provide bounds for the strong sensitivity constant.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/833e8fb254a92d0d5790e943769e5526651d6059

Citations in the corpus

• Inducing sensitivity on hyperspaces (2010, unknown): “Let A1 = [1,2] = [s1,a1].”