Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 309, Issue 1, Pages 155-192Publisher
SPRINGER
DOI: 10.1007/s00220-011-1365-z
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Funding
- NSF [DMS-0901627, IIS-1018433]
- Direct For Computer & Info Scie & Enginr [1018433] Funding Source: National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0901627] Funding Source: National Science Foundation
- Div Of Information & Intelligent Systems [1018433] Funding Source: National Science Foundation
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Consider a generic one-parameter unfolding of a homoclinic tangency of an area preserving surface diffeomorphism. We show that for many parameters (residual subset in an open set approaching the critical value) the corresponding diffeomorphism has a transitive invariant set Omega of full Hausdorff dimension. The set Omega is a topological limit of hyperbolic sets and is accumulated by elliptic islands. As an application we prove that a stochastic sea of the standard map has full Hausdorff dimension for sufficiently large topologically generic parameters.
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