Čech cohomology of attractors of discrete dynamical systems

Borsuk, 1968, Concerning homotopy properties of compacta, Fund. Math., 62, 223, 10.4064/fm-62-3-223-254 Borsuk, 1975, Theory of Shape, vol. 59 Dydak, 1978, Shape Theory: An Introduction, vol. 688 Giraldo, 2005, Shape of global attractors in topological spaces, Nonlinear Anal. Theory Methods Appl., 60, 837, 10.1016/j.na.2004.03.036 Gobbino, 2000, Topological properties of attractors for dynamical systems, Topology, 40, 279, 10.1016/S0040-9383(99)00061-0 Günther, 1993, Every attractor of a flow on a manifold has the shape of a finite polyhedron, Proc. Amer. Math. Soc., 119, 321, 10.2307/2159860 Hastings, 1979, A higher dimensional Poincaré–Bendixson theorem, Glas. Mat., 34, 263 Hatcher, 2002 Jezierski, 2005 Jiang, 2002, Uniqueness and attractivity of the carrying simplex for discrete-time competitive dynamical systems, J. Differential Equations, 186, 611, 10.1016/S0022-0396(02)00025-6 Jiang, 2009, Smoothness of the carrying simplex for discrete-time competitive dynamical systems: a characterization of neat embedding, J. Differential Equations, 246, 1623, 10.1016/j.jde.2008.10.008 Kapitanski, 2000, Shape and Morse theory of attractors, Comm. Pure Appl. Math., 53, 218, 10.1002/(SICI)1097-0312(200002)53:2<218::AID-CPA2>3.0.CO;2-W Le Calvez, 2010, Fixed point index of the iterates of R3-homeomorphisms at fixed points which are isolated invariant sets, J. Lond. Math. Soc., 83, 683, 10.1112/jlms/jdq050 Milnor, 1962, On axiomatic homology theory, Pacific J. Math., 12, 337, 10.2140/pjm.1962.12.337 Mardešić, 1982 Morón, 2006, A note about the shape of attractors of discrete semidynamical systems, Proc. Amer. Math. Soc., 134, 2165, 10.1090/S0002-9939-06-08305-5 Ortega, 2011, Attractors with vanishing rotation number, J. Eur. Math. Soc. (JEMS), 13, 1569 Ruiz-Herrera, 2012, Topological criteria of global attraction with applications in population dynamics, Nonlinearity, 25, 2823, 10.1088/0951-7715/25/10/2823 J.J. Sánchez-Gabites, On the Borsuk shape of attractors of discrete dynamical systems, preprint. Shen, 2008, Carrying simplices in nonautonomous and random competitive Kolmogorov systems, J. Differential Equations, 245, 1, 10.1016/j.jde.2008.03.024