Publications by Brian Coomes
- Transversal Connecting Orbits from Shadowing,
Numerische Mathematik
106
(2007)
427--469
(with Hüseyin Koçak and Kenneth J. Palmer)
- Shadowing in ODE's,
Rendiconti del Seminario Matematico
65
(2007)
89--114
(with Hüseyin Koçak and Kenneth J. Palmer, I am the third author).
- Homoclinic Shadowing,
Journal of Dynamics and Differential Equations
17
(2005),
175--215 (with Hüseyin Koçak
and Kenneth J. Palmer).
-
Computation of long periodic orbits in chaotic dynamical
systems, The Australian Mathematical Society Gazette 24 (1997),
183--190 (with Hüseyin Koçak and Kenneth J. Palmer).
-
Long periodic shadowing, Numerical Algorithms 14
(1997), 55--78 (with Hüseyin Koçak and Kenneth J. Palmer).
-
Shadowing orbits of ordinary differential equations on
invariant submanifolds, Transactions of the American Mathematical
Society 349 (1997), 203--216.
-
Shadowing in discrete dynamical systems, in "Six Lectures
on Dynamical Systems," World Scientific, Singapore (1996), 163--211.
(with Hüseyin Koçak and Kenneth J. Palmer)
-
On the torsion part of C^[n] with respect to
the action of a derivation, Proceedings of the American
Mathematical Society 123 (1995), 2191--2197.
-
Rigorous computational shadowing of orbits of ordinary
differential equations, Numerische Mathematik 69 (1995),
401--421 (with Hüseyin Koçak and Kenneth J. Palmer).
-
A Shadowing Theorem for ordinary differential
equations, Zeitschrift fur angewandte Mathematik und Physik
46 (1995), 85--106
(with Hüseyin Koçak and Kenneth J. Palmer).
-
Shadowing orbits of ordinary differential equations,
Journal of Computational and Applied Mathematics 52 (1994),
35--43 (with Hüseyin Koçak and Kenneth J. Palmer).
-
Periodic shadowing, in "Chaotic Numerics," Proceedings
of Chaotic Numerics: An International Workshop on the Approximation
and Computation of Complicated Dynamical Behavior, Contemporary
Mathematics 172 (1994), 115--130, American Mathematical
Society, Providence, Rhode Island (with Hüseyin Koçak and
Kenneth J. Palmer).
-
P-symmetries of two-dimensional p-f vector fields,
Differential and Integral Equations 5 (1992), 461--480.
-
Linearization of polynomial flows and spectra of
derivations, Journal of Dynamics and Differential
Equations 3 (1991), 29--66 (with Victor Zurkowski).
-
Polynomial flows on C^n, Transactions of the
American Mathematical Society 302 (1990), 493--506.
-
The Lorenz system does not have a polynomial flow,
Journal of Differential Equations 82 (1989),
386--407.
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