TY - JOUR

T1 - Theory of pseudo-orbit shadowing in dynamical systems

AU - Pilyugin, S. Yu

N1 - Funding Information: The research was supported by the Russian Foundation for Basic Research (grants nos. 02-01-01675 and 05-01-01079); CRC701 “Spectral Structures and Topological Methods in Mathematics,” Univ. of Bielefeld (Germany); JSPS, grant no. S-0318 (Japan); The Abdus Salam ICTP, Trieste (Italy); NSC, grant no. 98-28U-M-002-061 (Taiwan); and the P.L. Chebyshev Laboratory (the Faculty of Mechanics and Mathematics of St. Petersburg State University). Copyright: Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2011/12

Y1 - 2011/12

N2 - This is a survey of the main results obtained in the theory of pseudo-orbit shadowing in dynamical systems in the first decade of the 21st century. The main directions are shadowing and structural stability, C 1-interiors of sets of systems with the shadowing property, shadowing properties equivalent to the structural stability, and the denseness problem.

AB - This is a survey of the main results obtained in the theory of pseudo-orbit shadowing in dynamical systems in the first decade of the 21st century. The main directions are shadowing and structural stability, C 1-interiors of sets of systems with the shadowing property, shadowing properties equivalent to the structural stability, and the denseness problem.

UR - http://www.scopus.com/inward/record.url?scp=84856859951&partnerID=8YFLogxK

U2 - 10.1134/S0012266111130040

DO - 10.1134/S0012266111130040

M3 - Article

AN - SCOPUS:84856859951

VL - 47

SP - 1929

EP - 1938

JO - Differential Equations

JF - Differential Equations

SN - 0012-2661

IS - 13

ER -