The Conley index theory: A brief introduction
Banach Center Publications (1999)
- Volume: 47, Issue: 1, page 9-19
- ISSN: 0137-6934
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top- [1] M. Carbinatto, J. Kwapisz, and K. Mischaikow, Horseshoes and the Conley Index Spectrum, http://www.math.gatech.edu/ mischaik. Zbl0971.37005
- [2] M. Carbinatto and K. Mischaikow, Horseshoes and the Conley Index Spectrum (II): The theorem is sharp, http://www.math.gatech.edu/ mischaik. Zbl0954.37009
- [3] L. Arnold, C. Jones, K. Mischaikow, and G. Raugel, Dynamical Systems: Montecatini Terme, 1994, R. Johnson, ed. Lect. Notes in Math. 1609, Springer 1995.
- [4] C. Conley, Isolated Invariant Sets and the Morse Index. CBMS Lecture Notes 38, A.M.S. Providence, R.I. 1978.
- [5] C. Conley, A qualitative singular perturbation theorem, in: Global Theory of Dynamical Systems, (eds. Z. Nitecki and C. Robinson), Lecture Notes in Math. 819, Springer, 1980, 65-89.
- [6] C. Conley and R. Easton, Isolated invariant sets and isolating blocks, Trans. AMS 158 (1971), 35-61. Zbl0223.58011
- [7] C. Conley and J. Smoller, Viscosity matrices for two dimensional nonlinear hyperbolic systems, Comm. Pure Appl. Math. 23 (1970), 867-884. Zbl0201.43301
- [8] C. Conley and J. Smoller, Viscosity matrices for two dimensional nonlinear hyperbolic systems, II, Amer. J. Math. 94 (1972), 631-650. Zbl0247.35081
- [9] C. Conley and J. Smoller, On the structure of magnetohydrodynamic shock waves, Comm. Pure Appl. Math. 27 (1974), 367-375. Zbl0284.76080
- [10] C. Conley and J. Smoller, On the structure of magnetohydrodynamic shock waves, II, J. Math. Pures et Appl. 54 (1975), 429-444. Zbl0292.76045
- [11] M. Degiovanni and M. Mrozek, The Conley index for maps in the absence of compactness, Proc. Roy. Soc. Edin. 123A (1993), 75-94. Zbl0789.58066
- [12] A. Floer, A refinement of the Conley index and an application to the stability of hyperbolic invariant sets, Erg. Thy. Dyn. Sys. 7 (1987), 93-103. Zbl0633.58040
- [13] A. Floer, Proof of the Arnold conjecture for surfaces and generalizations to certain Kähler manifolds, Duke Math. J. 53 (1986), 1-32. Zbl0607.58016
- [14] J. Franks and D. Richeson, Shift Equivalence and the Conley Index, preprint 1998.
- [15] R. Franzosa, Index filtrations and the homology index braid for partially ordered Morse decompositions, Trans. AMS 298 (1986), 193-213. Zbl0626.58013
- [16] R. Franzosa, The connection matrix theory for Morse decompositions, Trans. AMS 311 (1989), 561-592. Zbl0689.58030
- [17] R. Franzosa, The continuation theory for Morse decompositions and connection matrices, Trans. AMS 310, (1988), 781-803. Zbl0708.58021
- [18] R. Franzosa and K. Mischaikow, The connection matrix theory for semiflows on (not necessarily locally compact) metric spaces, Journal of Differential Equations 71 (1988), 270-287. Zbl0676.54048
- [19] R. Franzosa and K. Mischaikow, Algebraic Transition Matrices in the Conley Index Theory, Trans. AMS 350 (1998), 889-912. Zbl0896.58053
- [20] T. Gedeon, H. Kokubu, K. Mischaikow, H. Oka, and J. Reineck, The Conley index for fast slow systems I: One dimensional slow variable, J. Dyn. Diff. Eq. (to appear). Zbl0945.34029
- [21] T. Kaczynski and M. Mrozek, Conley index for discrete multi-valued dynamical systems, Top. Appl. 65 (1995), 83-96. Zbl0843.54042
- [22] T. Kaczynski and M. Mrozek, Stable Index Pairs for Discrete Dynamical Systems, Bul. Can. Math. Soc. (to appear). Zbl0903.54018
- [23] C. McCord, Mappings and homological properties in the homology Conley index. Erg. Th. Dyn. Sys. 8* (1988), 175-198. Zbl0633.58019
- [24] C. McCord and K. Mischaikow, Connected simple systems, transition matrices, and heteroclinic bifurcations, Trans. AMS 333 (1992), 379-422. Zbl0763.34028
- [25] C. McCord and K. Mischaikow, On the global dynamics of attractors for scalar delay equations, Jour. AMS 9 (1996), 1095-1133. Zbl0861.58023
- [26] C. McCord, K. Mischaikow, and M. Mrozek. Zeta functions, periodic trajectories, and the Conley index, JDE 121 (1995), 258-292. Zbl0833.34045
- [27] K. Mischaikow, Global asymptotic dynamics of gradient-like bistable equations, SIAM Math. Anal. 26 (1995), 1199-1224. Zbl0841.35014
- [28] K. Mischaikow and Y. Morita, Dynamics on the Global Attractor of a Gradient Flow arising in the Ginzburg-Landau Equation, Jap. J. Ind. Appl. Math. 11 (1994), 185-202. Zbl0807.58029
- [29] K. Mischaikow and M. Mrozek, Isolating Neighborhoods and Chaos, Jap. J. Ind. Appl. Math. 12 (1995), 205-236. Zbl0840.58033
- [30] K. Mischaikow and M. Mrozek, Chaos in the Lorenz Equations: a Computer Assisted Proof, Bull. AMS 32 (1995), 66-72. Zbl0820.58042
- [31] K. Mischaikow and M. Mrozek, Chaos in the Lorenz Equations: a Computer Assisted Proof. Part II, Details, Math. Comp. 67 (1998), 1023-1046. Zbl0913.58038
- [32] K. Mischaikow, M. Mrozek, and J. Reineck, Singular Index Pairs, J. Dyn. Diff. Eq. (to appear). Zbl0943.34028
- [33] K. Mischaikow, M. Mrozek, J. Reiss, and A. Szymczak, Construction of Symbolic Dynamics from Experimental Time Series, http://www.math.gatech.edu/ mischaik.
- [34] K. Mischaikow, M. Mrozek, A. Szymczak, and J. Reiss, From Time Series to Symbolic Dynamics: An Algebraic Topological Approach, http://www.math.gatech.edu/ mischaik.
- [35] M. Mrozek, Leray functor and cohomological index for discrete dynamical systems, Trans. A. M. S. 318 (1990), 149-178. Zbl0686.58034
- [36] M. Mrozek, Topological invariants, multivalued maps, and computer assisted proofs, Comp. Math. 32 (1996), 83-104. Zbl0861.58027
- [37] M. Mrozek and K. P. Rybakowski, A cohomological Conley index for discrete dynamical systems, J. D. E. 90 (1991), 143-171. Zbl0721.58040
- [38] J. Reineck, Connecting orbits in one-parameter families of flows, Ergodic Theory and Dynamical Systems 8* (1988), 359-374. Zbl0675.58034
- [39] D. Richeson, Connection Matrix Pairs for the Discrete Conley Index, preprint 1997.
- [40] J. W. Robbin and D. Salamon, Dynamical systems, shape theory and the Conley index, Ergodic Theory and Dynamical Systems 8* (1988), 375-393. Zbl0682.58040
- [41] J. W. Robbin and D. Salamon, Lyapunov maps, simplicial complexes and the Stone functor, Ergod. Th. Dyn. Sys. 12 (1992), 153-183. Zbl0737.58033
- [42] K. P. Rybakowski, The Homotopy Index and Partial Differential Equations, Universitext, Springer-Verlag 1987. Zbl0628.58006
- [43] D. Salamon, Connected simple systems and the Conley index of isolated invariant sets, Trans. A.M.S. 291 (1985), 1-41. Zbl0573.58020
- [44] A. Szymczak, The Conley Index for Discrete Semidynamical Systems, Top. App. 66 (1995), 215-240. Zbl0840.34043
- [45] A. Szymczak, The Conley Index and Symbolic Dynamics, Topology 35 (1996), 287-299. Zbl0855.58023
- [46] A. Szymczak, A combinatorial procedure for finding isolating neighbourhoods and index pairs, Proc. Roy. Soc. Edin., to appear. Zbl0882.54032
- [47] T. Ważewski, Sur un principe topologique de l'examen de l'allure asymptotique des intégrales des équations différentielles ordinaires, Ann. Soc. Pol. Mat. 29 (1947), 279-313. Zbl0032.35001