Journal
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS
Volume 267, Issue 1, Pages 76-90Publisher
MAIK NAUKA/INTERPERIODICA/SPRINGER
DOI: 10.1134/S0081543809040063
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Funding
- NSF [DMS-0901627, DMS-0701271]
- Direct For Mathematical & Physical Scien [0901627] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [0901627] Funding Source: National Science Foundation
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We study generic unfoldings of homoclinic tangencies of two-dimensional area-preserving diffeomorphisms (conservative New house phenomena) and show that they give rise to invariant hyperbolic sets of arbitrarily large Hausdorff dimension. As applications, we discuss the size of the stochastic layer of a standard map and the Hausdorff dimension of invariant hyperbolic sets for certain restricted three-body problems. We avoid involved technical details and only concentrate on the ideas of the proof of the presented results.
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