Abstract
The method described here relies on interval arithmetic and graph theory to compute guaranteed coverings of strange attractors like Hénon attractor. It copes with infinite intervals, using either a geometric method or a new directed projective interval arithmetic.
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References
M. Barnsley. Fractals everywhere. Academic Press, 1988.
T. Cormen, C. Leiserson, and R. Rivest. Introduction to Algorithms. MIT Press, Cambridge, Massachusets, 1990.
J-F. Colonna. Kepler, von Neumann and God. The Visual Computer, 12: 346–349, 1996.
Z. Galias. Rigorous numerical studies of the existence of periodic orbits for the Hénon map. J. Universal Computer Science, 4 (2): 114–124, 1997.
M. Hénon. Numerical study of quadratic area-preserving mappings. Quart. Applied Math., (27): 291–312, 1969.
M. Hénon. A two dimensional map with a strange attractor. Commun. Math. Phys., 50: 69–77, 1976.
A. Neumaier. The wrapping effect, ellipsoid arithmetic, stability and confidence regions. Comput. Supplementum, 9: 175–190, 1993.
A. Neumaier and T. Rage. Rigorous chaos verification in discrete dynamical systems. Physica D, 67: 327–346, 1993.
E. Ott. Chaos in dynamical systems Cambridge University Press, 1993.
M. Pichat and J. Vignes. CADNA: a tool for studying chaotic behavior in dynamical systems. Proc. Real Numbers and Computers, Ecole des Mines, St-Etienne, France, April 4–6, 1995.
T. Rage, A. Neumaier and C. Schlier. Rigorous verification of chaos in a molecular model. Phys. Rev. E., 50, 2682–2688, 1994.
C. Robinson. Dynamical systems: stability, symbolic dynamics, and chaos. CRC Press, 1995.
J. Stolfi. Oriented Projective Geometry. Academic Press, 1991.
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Michelucci, D. (2001). Reliable Representations of Strange Attractors. In: Krämer, W., von Gudenberg, J.W. (eds) Scientific Computing, Validated Numerics, Interval Methods. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6484-0_31
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DOI: https://doi.org/10.1007/978-1-4757-6484-0_31
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