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References
O. Aberth, Precise Numerical Analysis, William C. Brown Publishers, Dubuque, Iowa, 1988.
C. Conley, On a generalization of the Morse index, in Ordinary Differential Equations, 1971 NRL-MRC Conference, ed. L. Weiss, Academic Press, New York, 27–33 (1972).
B.M. Garay, Discretization and some qualitative properties of ordinary differential equations about equilibria, Acta Math. Univ. Comeniane, 62, 249–275 (1993).
B.M. Garay, On structural stability of ordinary differential equations with respect to discretization methods, preprint.
L. Górniewicz, Topological Degree of Morphisms and its Applications to Differential Inclusions, Raccolta di Seminari del Dipartimento di Matematica dell'Universita degli Studi delta Calabria, No. 5, 1983.
S.P. Hastings, W.C. Troy, A shooting approach to the Lorenz equations, Bull. AMS, 27, 298–303 (1992).
B. Hassard and J. Zhang, Existence of a homoclinic orbit of the Lorenz system by precise shooting, SIAM J. Math. Anal., 25, 179–196 (1994).
B. Hassard, S.P. Hastings, W.C. Troy, J. Zhang, A computer proof that the Lorenz equations have “chaotic” solutions, Appl. Math. Letter, to appear.
T. Kaczyński and M. Mrozek, Conley index for discrete multivalued dynamical systems, Topology & its Appl, accepted.
K. Mischaikow and M. Mrozek, Isolating neighbourhoods and Chaos, accepted.
K. Mischaikow and M. Mrozek, Chaos in Lorenz equations: a computer assisted proof, Bull. AMS, in print.
K. Mischaikow and M. Mrozek, Chaos in Lorenz equations: a computer assisted proof, Part II: details, in preparation.
M. Mrozek, Leray Functor and the Cohomological Conley Index for Discrete Dynamical Systems, Transactions of the American Mathematical Society, 318, 149–178 (1990).
M. Mrozek, Topological invariants, multivalued maps and computer assisted proofs in dynamics, in preparation.
M. Mrozek, J. Reineck, R. Srzednicki, The Conley index over S1, in preparation.
M. Mrozek and K.P. Rybakowski, Discretized ordinary differential equations and the Conley index, J. of Dynamics and Differential Equations, 4, 57–63 (1992).
A. Neumaier, Th. Rage, Rigorous chaos verification in discrete dynamical systems, Physica D, 67, 327–346 (1993).
Th. Rage, A. Neumaier, Ch. Schlier, Rigorous verification of chaos in a molecular model, Physical Rev. E50, 2682–2688 (1994).
A.M. Stuart, Numerical analysis of dynamical systems, Acta Numerica, in print.
A. Szymczak, The Conley index and symbolic dynamics, preprint.
P. Zgliczyiiski, Fixed point index for iterations of maps, topological horseshoe and chaos, preprint.
P. Zgliczyński, in preparation. *** DIRECT SUPPORT *** A3418380 00006
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© 1995 Springer-Verlag
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Mrozek, M. (1995). Rigorous numerics of chaotic dynamical systems. In: Garbaczewski, P., Wolf, M., Weron, A. (eds) Chaos — The Interplay Between Stochastic and Deterministic Behaviour. Lecture Notes in Physics, vol 457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60188-0_61
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DOI: https://doi.org/10.1007/3-540-60188-0_61
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