Hyperbolicity, stability, and the criterion of homoclinic points.
Hayashi, Shuhei (1998)
Documenta Mathematica
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Hayashi, Shuhei (1998)
Documenta Mathematica
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Glushkova, D.I., Romanov, V.G. (2003)
Sibirskij Matematicheskij Zhurnal
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Pei-Dong Liu (1997)
Manuscripta mathematica
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J. Iglesias, A. Portela, A. Rovella (2009)
Fundamenta Mathematicae
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A new concept of stability, closely related to that of structural stability, is introduced and applied to the study of C¹ endomorphisms with singularities. A map that is stable in this sense is conjugate to each perturbation that is equivalent to it in a geometric sense. It is shown that this kind of stability implies Axiom A and Ω-stability, and that every critical point is wandering. A partial converse is also shown, providing new examples of C³ structurally stable maps.
J. Palis (2005)
Annales de l'I.H.P. Analyse non linéaire
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Bradul, Nataliya, Shaikhet, Leonid (2007)
Discrete Dynamics in Nature and Society
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Czeslaw Olech (1964)
Annales de l'institut Fourier
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Janina Kłapyta (1991)
Annales Polonici Mathematici
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Vrkoč, I.
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S. A. Ahmadi, M. R. Molaei (2013)
Annales Polonici Mathematici
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We introduce the notion of exponential limit shadowing and show that it is a persistent property near a hyperbolic set of a dynamical system. We show that Ω-stability implies the exponential limit shadowing property.
Delshams, Amadeu, Ramírez-Ros, Rafael (1999)
Experimental Mathematics
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