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2012 | 10 | 6 | 2088-2109
Tytuł artykułu

Global bifurcation of homoclinic trajectories of discrete dynamical systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove the existence of an unbounded connected branch of nontrivial homoclinic trajectories of a family of discrete nonautonomous asymptotically hyperbolic systems parametrized by a circle under assumptions involving topological properties of the asymptotic stable bundles.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
6
Strony
2088-2109
Opis fizyczny
Daty
wydano
2012-12-01
online
2012-10-12
Twórcy
autor
  • Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100, Toruń, Poland, robo@mat.umk.pl
Bibliografia
  • [1] Abbondandolo A., Majer P., On the global stable manifold, Studia Math., 2006, 177(2), 113–131 http://dx.doi.org/10.4064/sm177-2-2[Crossref]
  • [2] Alexander J.C., A primer on connectivity, In: Fixed Point Theory, Sherbrooke, June 2–21, 1980, Lecture Notes in Math., 886, Springer, Berlin-New York, 1981, 455–483
  • [3] Atiyah M.F., K-Theory, W.A. Benjamin, New York-Amsterdam, 1967
  • [4] Bachman G., Narici L., Functional Analysis, Dover, Mineola, 2000
  • [5] Bartsch T., The global structure of the zero set of a family of semilinear Fredholm maps, Nonlinear Anal., 1991, 17(4), 313–331 http://dx.doi.org/10.1016/0362-546X(91)90074-B[Crossref]
  • [6] Baskakov A.G., On the invertibility and the Fredholm property of difference operators, Math. Notes, 2000, 67(5–6), 690–698 http://dx.doi.org/10.1007/BF02675622[Crossref]
  • [7] Fitzpatrick P.M., Pejsachowicz J., The fundamental group of the space of linear Fredholm operators and the global analysis of semilinear equations, In: Fixed Point Theory and its Applications, Berkeley, August 4–6, 1986, Contemp. Math., 72, American Mathematical Society, Providence, 1988, 47–87 http://dx.doi.org/10.1090/conm/072/956479[Crossref]
  • [8] Fitzpatrick P.M., Pejsachowicz J., Rabier P.J., The degree of proper C 2 Fredholm mappings I, J. Reine Angew. Math., 1992, 427, 1–33
  • [9] Husemoller D., Fibre Bundles, 2nd ed., Grad. Texts in Math., 20, Springer, New York-Heidelberg, 1975
  • [10] Kato T., Perturbation Theory for Linear Operators, 2nd ed., Grundlehren Math. Wiss., 132, Springer, Berlin-New York, 1976 http://dx.doi.org/10.1007/978-3-642-66282-9[Crossref]
  • [11] Morris J.R., Nonlinear Ordinary and Partial Differential Equations on Unbounded Domains, PhD thesis, University of Pittsburgh, 2005
  • [12] Pejsachowicz J., Bifurcation of homoclinics, Proc. Amer. Math. Soc., 2008, 136(1), 111–118 http://dx.doi.org/10.1090/S0002-9939-07-09088-0[Crossref][WoS]
  • [13] Pejsachowicz J., Bifurcation of homoclinics of Hamiltonian systems, Proc. Amer. Math. Soc., 2008, 136(6), 2055–2065 http://dx.doi.org/10.1090/S0002-9939-08-09342-8[WoS][Crossref]
  • [14] Pejsachowicz J., Topological invariants of bifurcation, In: C*-Algebras and Elliptic Theory II, Trends Math., Birkhäuser, Basel, 2008, 239–250 http://dx.doi.org/10.1007/978-3-7643-8604-7_12[Crossref]
  • [15] Pejsachowicz J., Bifurcation of Fredholm maps I. Index bundle and bifurcation, Topol. Methods Nonlinear Anal., 2011, 38(1), 115–168
  • [16] Pejsachowicz J., Rabier P.J., Degree theory for C 1-Fredholm mappings of index 0, J. Anal. Math., 1998, 76, 289–319 http://dx.doi.org/10.1007/BF02786939
  • [17] Pejsachowicz J., Skiba R., Topology and homoclinic trajectories of discrete dynamical systems, preprint available at http://arxiv.org/abs/1111.1402 [WoS]
  • [18] Pötzsche C., Nonautonomous bifurcation of bounded solutions I: a Lyapunov-Schmidt approach, Discrete Contin. Dyn. Syst. Ser. B, 2010, 14(2), 739–776 http://dx.doi.org/10.3934/dcdsb.2010.14.739[Crossref]
  • [19] Pötzsche C., Bifurcation Theory, Munich University of Technology, 2010, preprint available at http://wwwm12.ma.tum.de/web/poetzsch/Christian_Potzsche_(Publications)/Publications_files/BifScript.pdf
  • [20] Pötzsche C., Nonautonomous bifurcation of bounded solutions II: A shovel-bifurcation pattern, Discrete Contin. Dyn. Syst. Ser. A, 2011, 31(3), 941–973 http://dx.doi.org/10.3934/dcds.2011.31.941[Crossref]
  • [21] Pötzsche C., Nonautonomous continuation of bounded solutions, Commun. Pure Appl. Anal., 2011, 10(3), 937–961 http://dx.doi.org/10.3934/cpaa.2011.10.937[Crossref]
  • [22] Rasmussen M., Towards a bifurcation theory for nonautonomous difference equation, J. Difference Equ. Appl., 2006, 12(3–4), 297–312 http://dx.doi.org/10.1080/10236190500489400[Crossref]
  • [23] Sacker R.J., The splitting index for linear differential systems, J. Differential Equations, 1979, 33(3), 368–405 http://dx.doi.org/10.1016/0022-0396(79)90072-X[Crossref]
  • [24] Secchi S., Stuart C.A., Global bifurcation of homoclinic solutions of Hamiltonian systems, Discrete Contin. Dyn. Syst., 2003, 9(6), 1493–1518 http://dx.doi.org/10.3934/dcds.2003.9.1493[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0121-8
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