Openness of the set of boundary preserving maps of an annulus with intermingled attracting basins |
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| Authors: | Yuli S Ilyashenko Victor A Kleptsyn Petr Saltykov |
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| Institution: | (1) Department of Mathematics, Cornell University, Ithaca, NY 14853, USA;(2) Steklov Mathematical Institute, Moscow State and Independent Universities, Moscow, Russia;(3) Moscow State University, Moscow, Russia;(4) University of Rennes, Rennes, France |
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| Abstract: | We prove that the set of smooth maps of an annulus with two attracting sets, both having metrically dense attracting basins,
is open in an appropriate function space. Thus a 1994 claim of I. Kan is justified.
To V. I. Arnold for more than half-centennial anniversary of his creative work, which in fluenced so many mathematicians,
including the authors of this paper |
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| Keywords: | " target="_blank"> Attractors basins density H?lder continuity Hausdorff dimension |
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