Conservative homoclinic bifurcations and some applications
Gorodetski A, Kaloshin V. 2009. Conservative homoclinic bifurcations and some applications. Proceedings of the Steklov Institute of Mathematics. 267(1), 76–90.
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Journal Article
| Published
| English
Author
Gorodetski, Anton;
Kaloshin, VadimISTA 
Abstract
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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Publishing Year
Date Published
2009-12-01
Journal Title
Proceedings of the Steklov Institute of Mathematics
Publisher
Springer Nature
Volume
267
Issue
1
Page
76-90
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Cite this
Gorodetski A, Kaloshin V. Conservative homoclinic bifurcations and some applications. Proceedings of the Steklov Institute of Mathematics. 2009;267(1):76-90. doi:10.1134/s0081543809040063
Gorodetski, A., & Kaloshin, V. (2009). Conservative homoclinic bifurcations and some applications. Proceedings of the Steklov Institute of Mathematics. Springer Nature. https://doi.org/10.1134/s0081543809040063
Gorodetski, Anton, and Vadim Kaloshin. “Conservative Homoclinic Bifurcations and Some Applications.” Proceedings of the Steklov Institute of Mathematics. Springer Nature, 2009. https://doi.org/10.1134/s0081543809040063.
A. Gorodetski and V. Kaloshin, “Conservative homoclinic bifurcations and some applications,” Proceedings of the Steklov Institute of Mathematics, vol. 267, no. 1. Springer Nature, pp. 76–90, 2009.
Gorodetski A, Kaloshin V. 2009. Conservative homoclinic bifurcations and some applications. Proceedings of the Steklov Institute of Mathematics. 267(1), 76–90.
Gorodetski, Anton, and Vadim Kaloshin. “Conservative Homoclinic Bifurcations and Some Applications.” Proceedings of the Steklov Institute of Mathematics, vol. 267, no. 1, Springer Nature, 2009, pp. 76–90, doi:10.1134/s0081543809040063.
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