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arXiv · 1106.1707

Nonuniformly expanding 1d maps with logarithmic singularities

Hiroki Takahasi·Qiudong Wang
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Abstract

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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Hiroki Takahasi, Qiudong Wang. 2011-06-09. Nonuniformly expanding 1d maps with logarithmic singularities. https://doi.org/10.1088/0951-7715%2F25%2F2%2F533

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