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Local dynamics near a heteroclinic tangency
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February
2018, 38(2): 431-448.
doi: 10.3934/dcds.2018020
An estimate on the Hausdorff dimension of stable sets of non-uniformly hyperbolic horseshoes
| 1. | Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS (UMR 7539), Villetaneuse, F-93439, France |
| 2. | IMPA, Instituto de Matemática Pura e Aplicada, 110, Estrada D. Castorina, CEP 22460-320, Rio de Janeiro, RJ, Brazil |
We show that the Hausdorff dimension of stable sets of non-uniformly hyperbolic horseshoes is strictly smaller than two.
Mathematics Subject Classification:
Primary: 37C29, 37E30; Secondary: 28D20.
Citation:
Carlos Matheus, Jacob Palis. An estimate on the Hausdorff dimension of stable sets of non-uniformly hyperbolic horseshoes. Discrete & Continuous Dynamical Systems,
2018, 38
(2)
: 431-448.
doi: 10.3934/dcds.2018020
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References:
| [1] |
C. Matheus, J. Palis and J. -C. Yoccoz, The Hausdorff dimension of stable sets of non-uniformly hyperbolic horseshoes, work in progress. Google Scholar |
| [2] |
J. Palis and J.-C. Yoccoz,
Non-uniformly hyperbolic horseshoes arising from bifurcations of Poincaré heteroclinic cycles, Publ. Math. Inst. Hautes Études Sci., 110 (2009), 1-217.
doi: 10.1007/s10240-009-0023-x. |
show all references
References:
| [1] |
C. Matheus, J. Palis and J. -C. Yoccoz, The Hausdorff dimension of stable sets of non-uniformly hyperbolic horseshoes, work in progress. Google Scholar |
| [2] |
J. Palis and J.-C. Yoccoz,
Non-uniformly hyperbolic horseshoes arising from bifurcations of Poincaré heteroclinic cycles, Publ. Math. Inst. Hautes Études Sci., 110 (2009), 1-217.
doi: 10.1007/s10240-009-0023-x. |
Figure 2.
Local dynamics near the parabolic tongues
Figure 3.
Simple composition of affine-like maps
Figure 4.
Parabolic composition of affine-like maps
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