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April  2013, 6(4): 1077-1094. doi: 10.3934/dcdss.2013.6.1077

Topology and homoclinic trajectories of discrete dynamical systems

1. 

Dipartamento di Matematica

2. 

Politecnico di Torino

3. 

Corso Duca Degli Abruzzi 24, 10129 Torino

4. 

Faculty of Mathematics and Computer Science

5. 

Nicolaus Copernicus University

6. 

Chopina 12/18, 87-100 Toru?

Received  August 2011 Revised  October 2011 Published  December 2012

We show that nontrivial homoclinic trajectories ofa family of discrete, nonautonomous, asymptotically hyperbolic systems parametrized by a circlebifurcate from a stationary solution if the asymptotic stable bundles $E^s(+\infty)$ and$E^s(-\infty)$ of the linearization at the stationary branch are twisted in different ways.
Citation: Jacobo Pejsachowicz, Robert Skiba. Topology and homoclinic trajectories of discrete dynamical systems. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 1077-1094. doi: 10.3934/dcdss.2013.6.1077
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show all references

References:
[1]

Math. Z., 243 (2003), 525-562. doi: 10.1007/s00209-002-0473-z.  Google Scholar

[2]

Studia Math., 177 (2006), 113-131. doi: 10.4064/sm177-2-2.  Google Scholar

[3]

Benjamin, New York, 1967.  Google Scholar

[4]

Nonlinear Analysis, 17 (1991), 313-331. doi: 10.1016/0362-546X(91)90074-B.  Google Scholar

[5]

Mathematical Notes, 67 (2000), 690-698. doi: 10.1007/BF02675622.  Google Scholar

[6]

Ann. Sci. Math. Québec, 22 (1998), 131-148.  Google Scholar

[7]

Nonlinear Analysis Forum, 6 (2001), 35-47.  Google Scholar

[8]

J. Functional Analysis, 8 (1971), 321-340.  Google Scholar

[9]

Contemporary Mathematics, 72 (1988). doi: 10.1090/conm/072/956479.  Google Scholar

[10]

J. Difference Equ. Appl., 10 (2004), 257-297. doi: 10.1080/10236190310001634794.  Google Scholar

[11]

Springer Verlag, 1975.  Google Scholar

[12]

Grundlehren der mathematischen Wissenschaften, 132, Springer, Berlin etc., 1980.  Google Scholar

[13]

Graduate Text in Mathematics, 160, Springer-Verlag, 1995. doi: 10.1007/978-1-4612-4182-9.  Google Scholar

[14]

Proc. Amer. Math. Soc., 136 (2008), 111-118. doi: 10.1090/S0002-9939-07-09088-0.  Google Scholar

[15]

Proc. Amer. Math. Soc., 136 (2008), 2055-2065. doi: 10.1090/S0002-9939-08-09342-8.  Google Scholar

[16]

Topol. Methods Nonlinear Anal., 38 (2011), 115-168.  Google Scholar

[17]

Journal d'Analyse Mathematique, 76 (1998), 289-319. doi: 10.1007/BF02786939.  Google Scholar

[18]

Central European Journal of Mathematics, 10 (2012), 2088-2109.  Google Scholar

[19]

Discrete Contin. Dyn. Syst. Ser. B, 14 (2010), 739-776. doi: 10.3934/dcdsb.2010.14.739.  Google Scholar

[20]

Discrete Contin. Dyn. Syst. Ser. A, 31 (2011), 941-973. doi: 10.3934/dcds.2011.31.941.  Google Scholar

[21]

Communications in Pure and Applied Analysis, 10 (2011), 937-961. doi: 10.3934/cpaa.2011.10.937.  Google Scholar

[22]

J. Difference Equ. Appl., 12 (2006), 297-312. doi: 10.1080/10236190500489400.  Google Scholar

[23]

J. Diff. Eq., 33 (1979), 368-405. doi: 10.1016/0022-0396(79)90072-X.  Google Scholar

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