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.


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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