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Much of our knowledge concerning the dynamics of specific nonlinear
systems comes from numerical simulations. I am interested in developing
techniques - this includes both theory and algorithms - that allow us
to efficiently use the computer to rigorously verify the observed
dynamics.
-
Low Dimensional Dynamics
- Z. Arai
and
K. Mischaikow, Rigorous
Computations of Homoclinic Tangencies
(submitted).
- M.
Gameiro
, T.
Gedeon
, W. Kalies, H. Kokubu, K. Mischaikow, and H. Oka, Topological
Horseshoes of Travelling Waves for a Fast-Slow Predator-Prey System
(submitted).
- S. Day,
O.
Junge, and K.
Mischaikow, Towards
Automated Chaos Verification, (To appear in Proc. Equadiff 2003)
- K. Mischaikow, M.
Mrozek , and A.
Szymczak , Chaos in
the Lorenz equations: A computer assisted proof. Part III: Classical
Case Parameter Values
- K. Mischaikow and M.
Mrozek , Chaos
in the Lorenz equations: A computer assisted proof. Part II: Details (The
final version can be found in Mathematics of Computation, 67
(1998) 1023-1046)
-
Infinite Dimensional Dynamics
- S. Day,
J.-P. Lessard, and K.
Mischaikow, Validated
continuation for equilibria of PDEs,
(submitted).
- S. Day,
Y.
Hiraoka, K.
Mischaikow, and T. Ogawa, Rigorous
Numerics for Global Dynamics: a study of the Swift-Hohenberg
equation (The final version can be found in SIAM
Dynamical Systems, 4,
2005).
- S. Day,
O.
Junge, and K.
Mischaikow, A
Rigorous Numerical Method for the Global Analysis of Infinite
Dimensional Discrete Dynamical Systems The final version can
be found in SIAM
Dynamical Systems, 3,
2004).
- P.
Zgliczynski
and K. Mischaikow, Rigorous
Numerics for Partial Differential Equations: the Kuramoto-Sivashinsky
equation (The final version can be found in Foundations
of Comp. Math. 1 255-288.)
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