Nonuniformly expanding 1d maps with logarithmic singularities

Details Nonuniformly expanding 1d maps with logarithmic singularities Nonuniformly expanding 1d maps with logarithmic singularities

2011-06-09

arxiv.org/abs/1106.1707v1

Nonlinearity 25 (2012) 533-550

Mathematics

Dynamical Systems

17 pages, no figure

Scientific paper

For a certain parametrized family of maps on the circle with critical points and logarithmic singularities where derivatives blow up to infinity, we construct a positive measure set of parameters corresponding to maps which exhibit nonuniformly expanding behavior. This implies the existence of "chaotic" dynamics in dissipative homoclinic tangles in periodically perturbed differential equations.

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