Geodesic
Diffeomorphisms with Intermingled Attracting Basins
Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 4, pp. 60-71.

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We construct a diffeomorphism $F$ of a manifold with boundary into itself with the following property. The attractor of $F$ has two components, and the attracting basins of these components are dense in the phase space and have positive measure. We prove that the class of examples constructed in the paper has codimension infinity in the space of all diffeomorphisms of the same manifold.
Keywords: attractor of a diffeomorphism, intermingled basin, skew product, codimension infinity. 
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Yu. S. Ilyashenko. Diffeomorphisms with Intermingled Attracting Basins. Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 4, pp. 60-71. http://geodesic.mathdoc.fr/item/FAA_2008_42_4_a4/

[1] A. Bonifant, J. Milnor, Schwarzian Derivatives and Cylinder Maps, Preprint, 2007 | MR

[2] M. W. Hirsch, C. C. Pugh, M. Shub, Invariant Manifolds, Lecture Notes in Math., 583, Springer-Verlag, Berlin–New York, 1977 | DOI | MR | Zbl

[3] I. Kan, “Open sets of diffeomorphisms having two attractors, each with an everywhere dense basin”, Bull. Amer. Math. Soc., 31:1 (1994), 68–74 | DOI | MR | Zbl

[4] J. Palis, “A global perspective for non-conservative dynamics”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 22:4 (2005), 485–507 | DOI | MR | Zbl

[5] Ya. Pesin, Lectures on Partial Hyperbolicity and Stable Ergodicity, Zurich Lectures in Advanced Math., European Math. Soc., Zürich, 2004 | MR | Zbl

[6] Yu. Ilyashenko, V. Kleptsyn, P. Saltykov, “Openness of the set of boundary preserving maps of an annulus with intermingled attracting basins”, J. Fixed Point Theory Appl., 3:2 (2008), 449–463 | DOI | MR | Zbl