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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
W. Kalies, H. Kokubu,
K. Mischaikow, H. Oka, and Pl. Pilarczyk, A Database Schema for the
Analysis of Global Dynamics of Multiparameter Systems, SIAM J. Applied Dyn. Syst., 8 757 (2009).
 Z. Arai
and
K. Mischaikow, Rigorous
Computations
of Homoclinic Tangencies
(The final version can be found in SIAM
Dynamical Systems, 5
(2006) 280292.).
 M.
Gameiro
, T.
Gedeon
, W. Kalies, H. Kokubu, K.
Mischaikow, and H. Oka, Topological
Horseshoes
of Travelling Waves for a FastSlow PredatorPrey System
(The final version can be found in Jour.
Dyn. Diff. Eqns., 19
(2007) 623654.).
 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) 10231046)

Infinite Dimensional Dynamics
 S. MaierPaape, K. Mischaikow, and T. Wanner, Structure of the
CahnHilliard Equation on the square, Int.
J. Chaos Bif., 17
(2007) 1211263.
 S. Day,
J.P. Lessard, and K.
Mischaikow, Validated
continuation
for equilibria of PDEs,
(The final version can be found in SIAM
Numerical Anal., 45,
2007, 13981424).
 S. Day,
Y.
Hiraoka, K.
Mischaikow, and T. Ogawa, Rigorous
Numerics
for Global Dynamics: a study of the SwiftHohenberg
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 KuramotoSivashinsky
equation (The final version can be found in Foundations
of
Comp. Math. 1 255288.)
