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Subexponential instability in one-dimensional maps implies infinite invariant measure. (English) Zbl 1311.37032

Summary: We characterize dynamical instability of weak chaos as subexponential instability. We show that a one-dimensional, conservative, ergodic measure preserving map with subexponential instability has an infinite invariant measure, and then we present a generalized Lyapunov exponent to characterize subexponential instability.{
©2010 American Institute of Physics}

MSC:

37E05 Dynamical systems involving maps of the interval
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37A40 Nonsingular (and infinite-measure preserving) transformations
37B25 Stability of topological dynamical systems
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