Integrability and dynamical systems

  1. Integrability and Nonintegrability of ordinary differential equations
    A. Goriely, Advanced Series on Nonlinear Dynamics, Vol 19 World Scientific
    2001 (436 pages).
  2. Singularity confinement and algebraic integrability (PDF)
    S. Lafortune and A. Goriely. J. Math Phys 2004, 45, 1191-1208
  3. Singularity analysis and normal forms (PDF)
    A. Goriely 2001, Physica D 152-153, 124-144
  4. Necessary and sufficient conditions for finite-time blowup in systems of ordinary differential equations (PDF)
    A. Goriely and C. Hyde, 2000, Journal of Differential Equations 161, 422-448.
  5. A brief history of Kovalevskaya exponents and modern developments, (PDF)
    A. Goriely, 2000 Regular and Chaotic Dynamics.
  6. The role of complex-time singularities in chaotic dynamics, (PDF)
    A. Goriely and M. Tabor, 1998 Regular and Chaotic Dynamics, 3.
  7. Finite time blow-up in dynamical systems, (PDF)
    A. Goriely and C. Hyde 1998, Phys. Lett. A 250, 311-318.
  8. Integrability, partial integrability and nonintegrability for systems of ordinary differential equations (PDF)
    A. Goriely, J. Math. Phys. 1996. 37 (1996) 1871-1893.
  9. A simple solution to the nonlinear front problem, (PDF)
    A. Goriely Phys. Rev. Lett. 75 (1995) 2047-2050.
  10. A Melnikov vector for n-dimensional mappings, (PDF)
    T. Bountis, A. Goriely et M. Kolman Phys. Lett. A 206 (1995) 38-48
  11. The Singularity analysis for nearly integrable systems: Homoclinic intersections and local multivaluedness (PDF)
    A. Goriely et M. Tabor, Physica D. 85 (1995) 93-125.
  12. Painleve Analysis and Normal Forms
    L. Brenig and A. Goriely, 1994 in Computer Algebra and Differential Equations.
    (E. Tournier, Ed.), Cambridge University Press, pp.211-238.
  13. How to compute the Melnikov vector?
    A. Goriely and M. Tabor, 1994 in Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC'94,
    ACM Press, pp. 205-210.
  14. Investigation of Painleve property under time singularities transformations, (PDF)
    A. Goriely, J. Math. Phys. 33 (1992) 2728-2742.
  15. From weak to full Painleve property via time singularities transformations
    A. Goriely, 1992 in Chaotic Dynamics: Theory and Practice (T. Bountis, Ed.) Plenum Press, pp. 91-101.
  16. Algebraic degeneracy and partial integrability for systems of ordinary differential equations (PDF)
    A. Goriely and L. Brenig, Phys. Lett. A 145 (1990) 245.
  17. Quasimonomial Transformations and Decoupling
    L. Brenig and A. Goriely, 1991 in Soliton and Chaos (I. Antoniou and F. J. Lambert, Eds.)
    Research Reports in Physics, Springer Verlag.
  18. An algorithmic approach to differential equations
    A. Goriely, 1990 in Equations Differentielles et Calcul Formel (Strasbourg).
  19. Quasimonomial Transformations and Integrability
    L. Brenig and A. Goriely, 1990 in Partially Integrable Evolution Equations in Physics
    (Ed. R. Conte and N. Boccara, NATO ASI Series, Kluwer Academic Publisher), pp. 571-573.
  20. Universal canonical forms for time continuous dynamical systems (PDF)
    L. Brenig and A. Goriely, Phys. Rev. A 40 (1989) 4119.
Copyright 2006 Alain Goriely Photo credit: Piotr Pieranski