Papers by Warwick Tucker



  1. Rigorous Models for the Lorenz Flow (licentiat thesis)
    U:U:D:M Report 1996:26, ISSN 1101-3591.


  2. Transitivity of Lorenz-like Maps and the Tired Baker's Map
    Preprint, 1996.


  3. Non-uniformly expanding dynamics in maps with singularities and criticalities
    with S. Luzzatto, Publ. Math. IHES, 89, pp. 179-226, 1999.

  4. The Lorenz attractor exists (Ph.D. thesis)
    Uppsala Dissertations in Mathematics 11, 1998, ISBN 91-506-1296-4
    (revised 981207 and 990310)


  5. The Lorenz attractor exists (short version of my Ph.D. thesis)
    C. R. Acad. Sci. Paris, t. 328, SÚrie I, pp. 1197-1202, 1999.


  6. Computational algorithms for ordinary differential equations
    Proceedings from EquaDiff 99 Vol I, World Scientific, Singapore, pp. 71-76, 2000.


  7. A Rigorous ODE solver and Smale's 14th Problem
    Foundations of Computational Mathematics, 2:1, pp. 53-117, 2002.


  8. Computing accurate Poincare maps
    Physica D, 171, pp.127-137, 2002.
    [The program poincare.cc]


  9. 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]


  10. Robust normal forms for saddles of analytic vector fields
    Nonlinearity, 17, pp. 1965-1983, 2004.

  11. Validated Numerics for Pedestrians
    Proceedings from ECM'05 (Ed. A. Lapti),  pp. 851-860, 2005.

  12. Reconstructing Metabolic Networks Using Interval Analysis
    wirh V. Moulton. Lecture Notes in Comp. Sci., 3692, pp. 192-203, 2005.

  13. Parameter reconstruction for biochemical networks using interval analysis
    with V. Moulton. Reliable Computing, Volume 12, issue 5, pp. 389-402, 2006

  14. 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]


  15. Interval Analysis Techniques for Boundary Value Problems of Elasticity in Two Dimensions
    with I. Mitrea. J. Diff. Eq., 233, pp. 181-198, 2007.

  16. S-system parameter estimation for noisy metabolic profiles using Newton-flow analysis
  17. with Z. Kultaic and V. Moulton. IET Systems Biology, Volume 1, issue 3, pp. 174-180, 2007.
    [Supplementary material: supplement.pdf]

  18. Enclosing all zeros of an analytic function - a rigorous approach
  19. with T. Johnson. J. Comput. Appl. Math., Volume 228, Issue 1, pp. 418-423, 2008

  20. Rigorous parameter reconstruction for differential equations with noisy data
  21. with T. Johnson. Automatica, Volume 44, pp. 2422-2426, 2008.

  22. Rigorous study of short periodic orbits for the Lorenz system
  23. with Z. Galias. Proceedings of ISCAS, pp. 764-767, 2008.

  24. On a Fast and Accurate Method to Enclose All Zeros of an Analytic Function on a Triangulated Domain
  25. with T. Johnson. Submitted 2008.

  26. A Computer-assisted Proof of the Existence of Solutions to a Boundary Value Problem with an Integral Boundary Condition
  27. with O. Fogelklou, G. Kreiss, and M. Siklosi. Submitted, 2008.

  28. On a computer-aided approach to the computations of Abelian integrals
  29. with T. Johnson. Submitted, 2008.

  30. Short periodic orbits for the Lorenz system
  31. with Z. Galias. Proceedings of ICSES, pp. 285-288, 2008.

  32. A rigorous study of possible configurations of limit cycles bifurcating from a hyper-elliptic Hamiltonian of degree five
  33. with T. Johnson. Dynamical Systems - An International Journal, Volume 24 Issue 2, pp. 237-247, 2009.

  34. An improved lower bound on the number of limit cycles bifurcating from a quintic Hamiltonian planar vector field under quintic perturbation
  35. with T. Johnson. To appear in International Journal of Bifurcation and Chaos.

  36. Fundamentals of chaos
  37. Chapter 1 in "Intelligent Computing Based on Chaos", Springer Verlag, 2009.

  38. Symbolic dynamics based method for rigorous study of the existence of short cycles for chaotic systems
  39. with Z. Galias. Submitted, 2008.

  40. Automated computation of robust normal forms of planar analytic vector fields
  41. with T. Johnson. To appear in Discrete and continuous dynamical systems - B.

  42. Computable parametrisations of local invariant manifolds
  43. with T. Johnson. Submitted, 2009.

  44. A rigorous lower bound for the stability regions of the quadratic map
  45. with D. Wilczak. To appear in Physica D.

  46. An improved lower bound on the number of limit cycles bifurcating from a Hamiltonian planar vector field of degree 7
  47. with T. Johnson. Submitted, 2009.