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On Lyapunov exponent and sensitivity. (English) Zbl 1034.37019

Summary: Sensitive dependence on initial conditions is widely understood as being the central idea of chaos. For a large class of transformations of the interval, we prove that positiveness of the Lyapunov exponent implies the sensitivity property. We also provide bounds for the sensitivity constant.

MSC:

37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37E05 Dynamical systems involving maps of the interval
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