Nonautonomous Conley index theory. The homology index and attractor-repeller decompositions
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Nonautonomous differential equations, attractor-repeller decompositions, Morse-Conley index theory, nonautonomous Conley index, homology Conley indexAbstrakt
In a previous work, the author established a nonautonomous Conley index based on the interplay between a nonautonomous evolution operator and its skew-product formulation. This index is refined to obtain a Conley index for families of nonautonomous evolution operators. Different variants such as a categorial index, a homotopy index and a homology index are obtained. Furthermore, attractor-repeller decompositions and conecting homomorphisms are introduced for the nonautonomous setting.Bibliografia
M.C. Carbinatto and K.P. Rybakowski, Homology index braids in infinite-dimensional Conley index theory, Topol. Methods Nonlinear Anal. 26 (2005), 35–74.
R.D. Franzosa, The connection matrix theory for Morse decompositions, Trans. Amer. Math. Soc. 311 (1989).
R.D. Franzosa and K. Mischaikow, The connection matrix theory for semiflows on (not necessarily locally compact) metric spaces, J. Differential Equations 71 (1988), 270–287.
A. Jänig, A non-autonomous Conley index, J. Fixed Point Theory Appl. 19 (2017), 1825–1870.
K.P. Rybakowski, The homotopy index for semiflows, Trans. Amer. Math. Soc. 269 (1982), 351–382.
K.P. Rybakowski, The Homotopy Index and Partial Differential Equations, Springer, 1987.
E.H. Spanier, Algebraic Topology, McGraw–Hill, New York, 1966.
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