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Владимир Добрынский, Vladimir Dobrynskii (1998)
Об отсутствии циклов у унимодальных отображений квадрата@@@On the absence of cycles for unimodal mappings of the square, 63
M. Misiurewicz (1980)
STRANGE ATTRACTORS FOR THE LOZI MAPPINGSAnnals of the New York Academy of Sciences, 357
V. Dobrynskiy (1999)
On attractors of piecewise linear 2-endomorphismsNonlinear Analysis-theory Methods & Applications, 36
M. Hénon (1976)
A two-dimensional mapping with a strange attractorCommunications in Mathematical Physics, 50
Y. Pesin (1992)
Dynamical systems with generalized hyperbolic attractors: hyperbolic, ergodic and topological propertiesErgodic Theory and Dynamical Systems, 12
Владимир Добрынский, Vladimir Dobrynskii (1998)
Унимодальные отображения и хаос по Ли - Йорку@@@Unimodal mappings and Li - Yorke chaos, 63
V. Dobrynskiy (2000)
On a Phase Pattern Structure of Unimodal 2-Endomorphisms
Differential Equations, Vol. 41, No. 6, 2005, pp. 780–790. Translated from Differentsial'nye Uravneniya, Vol. 41, No. 6, 2005, pp. 746–754. Original Russian Text Copyright c 2005 by Dobrynskii. ORDINARY DIFFERENTIAL EQUATIONS On the Structure of Generalized Hyperbolic Attractors of Mappings That Are Not One-to-One V. A. Dobrynskii Institute of Metal Physics, National Academy of Sciences, Kiev, Ukraine Received November 26, 2001 Pesin [1] introduced a class of di eomorphisms with singularities which have generalized hyper- bolic attractors and established a number of properties of such di eomorphisms. Later, Sataev [2] developed the theory of di eomorphisms with singularities (under somewhat more restrictive con- ditions) up to so-called \natural" limits. However, the following problem remains open: how completely do the above-mentioned results describe the properties of nontrivial generalized hyper- bolic attractors of piecewise smooth mappings that are not one-to-one? This problem is nontrivial and has been little studied yet. To the best of the author's knowledge, the paper [3] is the only one in which, among other things, the existence of a nontrivial generalized hyperbolic attractor was proved for a certain piecewise linear endomorphism of a plane. The structure of this attrac- tor di ers dramatically from that of generalized
Differential Equations – Springer Journals
Published: Jul 27, 2005
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