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Lipschitz shadowing and structural stability of flows |
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| Authors: | Kenneth J Palmer Sergei Yu Pilyugin Sergey B Tikhomirov |
| Institution: | 1. Department of Mathematics, National Taiwan University, Taipei 106, Taiwan;2. Faculty of Mathematics and Mechanics, St. Petersburg State University, University av. 28, 198504 St. Petersburg, Russia;3. Departamento de Matematica, Pontificia Universidade Catolica do Rio de Janeiro, Rua Marques de Sao Vicente, 225, Edificio Cardeal Leme, sala 862, Gavea, Rio de Janeiro, CEP 22453-900, Brazil;4. Freie Universität Berlin, Institut für Mathematik I, Arnimallee 3 D, 14195, Berlin, Germany |
| Abstract: | Let ? be the flow generated by a smooth vector field X on a smooth closed manifold. We show that the Lipschitz shadowing property of ? is equivalent to the structural stability of X and that the Lipschitz periodic shadowing property of ? is equivalent to the Ω-stability of X. |
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