Recent work by Konstantin Mischaikow


Contents

Conley Index


Conley Index

Computational Homology

Computational Dynamics

Mathematical Biology

Computer Graphics

Home page

The Conley index is a topological generalization of Morse theory.

  • Survey Articles

    • K. Mischaikow and M. Mrozek Conley Index Theory. (The final version can be found in Handbook of Dynamical Systems II: Towards Applications, (B. Fiedler, ed.) North-Holland, 2002.
    • K. Mischaikow, The Conley Index Theory: A Brief Introduction .  (The final version can be found in Conley Index Theory, Banach Center Publications, 47, 1999.)
    • L. Arnold, C. Jones, K. Mischaikow, and G. Raugel, Dynamical Systems, Lecture Notes in Mathematics 1609 (R. Johnson ed.), Springer, 1995.
    • The structure of isolated invariant sets and the Conley Index, Contemporary Mathematics (ed. C. McCord), 152(1993), 269-290.
  • Structure of Invariant Sets

    • Theory

      • H. Kokubu, K. Mischaikow, and H. Oka, Directional Transition Matrix.  (The final version can be found in Conley Index Theory, Banach Center Publications, 47, 1999.)
      • K. Mischaikow and R. Franzosa, Algebraic transition matrices in the Conley Index theory, Trans. AMS, 350(3) (1998), 889-912.
      • C. McCord and K. Mischaikow, On the global dynamics of attractors for scalar delay equations, Journal AMS 9(4) (1996), 1095-1133.
      • C.  McCord and K. Mischaikow, Equivalence of topological and singular transition matrices in the Conley Index theory, Michigan Math. J. 42 (1995), 387-414.
      • C.  McCord and K. Mischaikow, Connected simple systems, transition matrices, and heteroclinic bifurcations, Trans. AMS 333(1) (1992), 397-422.
      • K. Mischaikow and R. Franzosa, The connection matrix theory for semiflows on (not necessarily locally compact) metric spaces, J. Diff. Eqns., 71(2) (1988), 270-287.
      • Existence of generalized homoclinic orbits for one parameter families of flows, Proc. Amer. Math. Soc., 103(1)(1988), 59-68.
    • Applications

      • Hiroshi Kokubu, K. Mischaikow, Yasumasa Nishiura, Hiroe Oka, and Takeshi Takaishi, Connecting orbit structure of monotone solutions in the shadow system (the final version can be found in JDE, 140 (1997) 309-364).
      • H. Kokubu, K. Mischaikow, H. Oka, Existence of infinitely many connecting orbits in a singularly perturbed ordinary differential equation, Nonlinearity 9 (1996), 1263-1280.
      • T. Gedeon and K. Mischaikow, Structure of the global attractor of cyclic feedback systems, J. Dyn. & Diff. Eq., 7(1)(1995), 141-190.
      • Global asymptotic dynamics of gradient-like bistable equations, SIAM J. Math. Anal., 26(5) (1995), 1199-1224.
      • K. Mischaikow and J. Reineck, Travelling waves in predator-prey systems, SIAM J. Math. Anal., 24 (1993), 1179-1214. 
      • V. Hutson and K. Mischaikow,  Travelling waves for mutualist species, SIAM J. Math. Anal., 24 (1993), 987-1008.
      • B. Fiedler and K. Mischaikow, Dynamics of bifurcations for variational problems with O(3) equivariance: A Conley index approach, Arch. Rat. Mech. Anal. 119 (1992), 145-196.
      • H. Hattori and K. Mischaikow, A dynamical system approach to a phase transition problem, J. Diff. Eqns., 94 (2)(1991), 340-378.
      • H. Hattori and K. Mischaikow, On the existence of intermediate magnetohydrodynamic shock waves, J. of Dyn. & Diff. Eqns., 2 (2)(1990), 163-175.
  • Singular Perturbations

    • Theory

  • Time Series

    • Theory

    • Applications








Last Modified on January 22, 2006

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