Sergei Yu. Pilyugin

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Publications

More than 150 scientific publications. List of main publications:
    Monographs:

  1. S.Yu.Pilyugin: Introduction to Structurally Stable Systems of Differential Equations, Leningr. Gos. Univ. (1988), 160 pp. (in Russian)
  2. S.Yu.Pilyugin: Introduction to Structurally Stable Systems of Differential Equations, Birkhauser Verlag, Basel-Boston-Berlin (1992). (revised translation of [I])
  3. S.Yu.Pilyugin: The Space of Dynamical Systems with the C0-Topology. Lecture Notes in Math., vol.1571, Springer-Verlag (1994).
  4. S.Yu.Pilyugin: Shadowing in Dynamical Systems. Lecture Notes in Math., vol.1706, Springer-Verlag (1999). 5. S.Yu.Pilyugin: Spaces of Dynamical Systems, R&C Dynamics (2008), 270 pp. (in Russian)
    Selected papers:

  1. S.Yu.Pilyugin: Systems of Morse-Smale type with identical phase diagrams, Differ. Equat., vol. 10, N5, 816-821 (1974). (in Russian)
  2. S.Yu.Pilyugin: Cycles in phase diagrams of Morse-Smale systems, Differ. Equat., vol. 13, N5, 874-882 (1977). (in Russian)
  3. S.Yu.Pilyugin: Phase diagrams that determine Morse-Smale systems without periodic trajectories on spheres, Differ. Equat., vol. 14, N2, 245-254 (1978). (in Russian)
  4. S.Yu.Pilyugin: Attracting sets with the strong transversality condition on the boundary, Differ. Equat., vol. 22, N9, 1532-1539 (1986). (in Russian)
  5. S.Yu.Pilyugin: Limit sets of trajectories of domains in dynamical systems, Funct. Anal. and Appl., vol. 23, N3, 82-83 (1989). (in Russian)
  6. R.Corless and S.Yu.Pilyugin: Approximate and real trajectories for generic dynamical systems, J. Math. Anal. Appl., vol. 189, 409-423 (1995).
  7. A.V.Babin and S.Yu.Pilyugin: Continuous dependence of an attractor on the shape of domain, Zap. Nauchn. Sem. POMI, vol. 221, 58-66 (1995).
  8. V.A.Pliss and S.Yu.Pilyugin: Persistent structures for diffeomorphisms with ergodic invariant measure, Dokl. Ross. AN, vol. 343, N3, 312-313 (1995). (in Russian)
  9. V.S.Afraimovich and S.Yu.Pilyugin: Special pseudotrajectories of lattice dynamical systems, Rand. and Comp. Dyn., vol. 4, N1, 29-47 (1996).
  10. T.Eirola and S.Yu.Pilyugin: Pseudotrajectories generated by a discretization of a parabolic equation, J. Dyn. Diff. Equat.,vol. 8, N2, 281-297 (1996).
  11. T.Eirola, O.Nevanlinna, and S.Yu.Pilyugin: Limit shadowing property, Numer. Funct. Anal. and Optim., vol. 18, no. 1-2, 75-92 (1997).
  12. S.Yu.Pilyugin: Shadowing in structurally stable flows, J. Diff. Equat., vol. 140, 238-265 (1997).
  13. E.V.Vasil'eva, V.A.Pliss, and S.Yu.Pilyugin: Local properties of planar homoclinic structures and the Hausdorff dimension, Differ. Equat., vol. 33, N5, 595-601 (1997). (in Russian)
  14. S.Yu.Pilyugin and O.B.Plamenevskaya: Shadowing is generic, Topology and Its Appl., vol. 97, N3, 253-266 (1999).
  15. I.N.Kostin and S.Yu.Pilyugin: Uniform exponential stability of perturbed attractors for evolution equations, Dokl. Ross. AN, vol. 369, N4, 449-450 (1999). (in Russian)
  16. S.Yu.Pilyugin: Inverse shadowing by continuous methods, Discr. Cont. Dyn. Syst., vol. 8, N1, 29-38 (2002).
  17. S.Yu.Pilyugin, A.A.Rodionova, and K.Sakai: Orbital and weak shadowing properties, Discr. Cont. Dyn. Syst., vol. 9, N2, 287-308 (2003).
  18. S.Yu.Pilyugin and S.B.Tikhomirov: Shadowing in actions of some Abelian groups, Fund. Math., vol. 179, 83-96 (2003).
  19. W.-J.Beyn and S.Yu.Pilyugin: Attractors of reaction diffusion systems on infinite lattices, J. Dyn. Diff. Equat., vol. 15, N2/3, 485-515 (2003).
  20. S.Yu.Pilyugin: C1-variant of Arnold's conjecture on limit sets of domains, Proc. St.Petersb. Math. Soc., vol. 10, 173-183 (2004). (in Russian)
  21. W.-J.Beyn, V.S.Kolezhuk, and S.Yu.Pilyugin: Convergence of discretized attractors for parabolic equations on the line, Zap. Nauchn. Sem. POMI, vol. 318, 14-41 (2004).
  22. S.Yu.Pilyugin: Generalizations of the notion of hyperbolicity, J. Difference Equat., vol 12, N3-4, 271-282 (2006).
  23. S.Yu.Pilyugin, K.Sakai, and O.A.Tarakanov: Transversality properties and C^1-open sets of diffeomorphisms with weak shadowing, Discr. Cont. Dyn. Syst., vol. 16, N4, 871-882 (2006).
  24. 4. S.Yu.Pilyugin and K.Sakai: C0 transversality and shadowing properties, Proc. Steklov Math. Inst., vol. 256, 290-305 (2007).
  25. S.Yu.Pilyugin: Sets of dynamical systems with various limit shadowing properties, J. Dyn. Diff. Equat., vol. 19, N3, 747-775 (2007).
  26. S.Yu.Pilyugin and J.Rieger: General hyperbolicity conditions for set-valued mappings, Zap. Nauchn. Semin. POMI, vol. 372, 172-186 (2009). (in Russian)
  27. S.Yu.Pilyugin and S.B.Tikhomirov: Sets of vector fields with various shadowing properties, Dokl. Ross. AN, vol. 422, N1, 30-31 (2008). (in Russian)
  28. S.Yu.Pilyugin and S.B.Tikhomirov: Vector fields with the oriented shadowing property, J. Diff. Equat., vol. 248, 1345-1375 (2010).
  29. A.V.Osipov, S.Yu.Piyugin, and S.B.Tikhomirov: Periodic shadowing and Omega-stability, Reg. & Chaotic Dynamics, vol. 15, N2-3, 404-417 (2010).
  30. S.Yu.Pilyugin: Variational shadowing, Discr. Cont. Dyn. Syst., ser. B, vol. 14, N2, 733-737 (2010).
  31. S.Yu.Pilyugin and S.B.Tikhomirov: Lipschitz shadowing implies structural stability, Nonlinearity, vol. 23, 2509-2515 (2010).