Open circle maps: Small hole asymptotics

Details Open circle maps: Small hole asymptotics Open circle maps: Small hole asymptotics

2011-12-22

arxiv.org/abs/1112.5390v1

Nonlinear Sciences

Chaotic Dynamics

6 pages, 2 figures

Scientific paper

We consider escape from chaotic maps through a subset of phase space, the hole. Escape rates are known to be locally constant functions of the hole position and size. In spite of this, for the doubling map we can extend the current best result for small holes, a linear dependence on hole size h, to include a smooth h^2 ln h term and explicit fractal terms to h^2 and higher orders. The results are confirmed by numerical simulations, followed by a discussion of the occurrence of h^2 ln h in more general chaotic maps.

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