Papers
by
Warwick Tucker
- Rigorous Models for
the
Lorenz Flow (licentiat
thesis)
U:U:D:M Report
1996:26, ISSN
1101-3591.
- Transitivity of
Lorenz-like Maps and the Tired Baker's Map
Preprint, 1996.
- Non-uniformly
expanding
dynamics in maps with singularities and criticalities
with S. Luzzatto,
Publ. Math.
IHES, 89, pp. 179-226, 1999.
- The Lorenz attractor exists
(Ph.D. thesis)
Uppsala
Dissertations in
Mathematics 11, 1998, ISBN 91-506-1296-4
(revised 981207 and
990310)
- The Lorenz
attractor exists (short
version of my Ph.D. thesis)
C. R. Acad. Sci.
Paris, t. 328,
Série I, pp. 1197-1202, 1999.
- Computational
algorithms for ordinary differential equations
Proceedings from
EquaDiff 99 Vol
I, World Scientific, Singapore, pp.
71-76, 2000.
- A Rigorous ODE solver and
Smale's
14th Problem
Foundations of
Computational
Mathematics, 2:1, pp. 53-117, 2002.
- Computing
accurate Poincare maps
Physica D, 171,
pp.127-137,
2002.
[The program
poincare.cc]
-
Some
Counterexamples for the Spectral Radius Conjecture
with I. Mitrea. Differential and Integral Equations, Vol 16, No 12,pp.
1409-1439, 2003.
[The program radius.cc]
-
Robust
normal forms for saddles of analytic vector fields
Nonlinearity, 17,
pp. 1965-1983,
2004.
- Validated Numerics
for
Pedestrians
Proceedings from
ECM'05 (Ed. A.
Lapti), pp. 851-860, 2005.
- Reconstructing
Metabolic Networks Using Interval Analysis
wirh V. Moulton.
Lecture Notes
in Comp. Sci.,
3692, pp. 192-203, 2005.
- Parameter
reconstruction for biochemical networks using interval analysis
with V. Moulton.
Reliable
Computing, Volume 12, issue 5, pp. 389-402, 2006
-
Estimating
parameters for generalized mass action models using constraint
propagation
with Z. Kutalik and V. Moulton.Mathematical Biosciences, 208, pp.
607-620, 2007.
[The program
publicGMAcode.tar]
- Interval
Analysis Techniques for Boundary Value Problems of Elasticity in Two
Dimensions
with I. Mitrea. J.
Diff. Eq., 233, pp. 181-198, 2007.
- S-system parameter estimation for
noisy metabolic
profiles using Newton-flow
analysis
with
Z.
Kultaic and V. Moulton. IET Systems Biology, Volume 1, issue 3, pp.
174-180, 2007.
[Supplementary material: supplement.pdf]
- Enclosing
all zeros of an analytic function - a rigorous approach
with
T.
Johnson. J. Comput. Appl. Math., Volume 228, Issue 1, pp. 418-423, 2008
- Rigorous parameter
reconstruction for differential equations with noisy data
with
T.
Johnson. Automatica, Volume 44, pp. 2422-2426, 2008.
- Rigorous study of short periodic
orbits for the Lorenz system
with
Z.
Galias. Proceedings of ISCAS, pp. 764-767, 2008.
- On a Fast and Accurate Method to
Enclose All Zeros of an Analytic Function on a Triangulated Domain
with
T.
Johnson. Submitted 2008.
- A Computer-assisted Proof of the
Existence of Solutions to a Boundary Value Problem with an Integral
Boundary Condition
with
O. Fogelklou, G. Kreiss, and M. Siklosi. Submitted, 2008.
- On a computer-aided approach to
the computations of Abelian integrals
with
T. Johnson. Submitted, 2008.
- Short periodic orbits for the
Lorenz system
with
Z. Galias. Proceedings of ICSES, pp. 285-288, 2008.
- A rigorous study of possible
configurations of limit cycles bifurcating
from a hyper-elliptic Hamiltonian of degree five
with
T. Johnson. Dynamical Systems - An International Journal, Volume 24
Issue 2, pp. 237-247, 2009.
- An improved lower bound on the
number of limit cycles bifurcating from a quintic Hamiltonian planar
vector field under quintic perturbation
with
T. Johnson. To appear in International Journal of Bifurcation and Chaos.
- Fundamentals of chaos
Chapter 1 in "Intelligent Computing Based on Chaos", Springer
Verlag, 2009.
-
Symbolic dynamics based method for rigorous study of the existence of
short cycles for chaotic systems
with
Z. Galias. Submitted, 2008.
- Automated computation of robust
normal forms of planar analytic vector fields
with
T. Johnson. To appear in Discrete and continuous dynamical systems - B.
-
Computable parametrisations of local invariant manifolds
with
T. Johnson. Submitted, 2009.
-
A rigorous lower bound for the stability regions of the quadratic map
with
D. Wilczak. To appear in Physica D.
-
An improved lower bound on the number of limit cycles bifurcating from a Hamiltonian planar vector field of degree 7
with T. Johnson. Submitted, 2009.