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Article Dans Une Revue International journal of bifurcation and chaos in applied sciences and engineering Année : 1999

GEOMETRY AND ORDER OF CHAOS

Jan Awrejcewicz
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  • PersonId : 940409
Kevin A. Broughan
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  • PersonId : 940410

Résumé

In the beginning a brief introduction to a symmetry increasing as well as to quantified geometrical structures of chaotic attractors have been given. Then, the research is focused on the Chossat-Golubitsky map. A saddle-node bifurcation on the boundary of the umbrella shape set of saddles, crises of two peculiar structures of saddles and an extremely high order of infinitely many flip and regular saddle orbits have been reported. The geometrical properties of hyperchaos and its relation to the Kakeya-Besicovitch and the Apollonian packing have been illustrated and discussed. A fractal organization of the successive periodic saddles and fractal normal forms have been described.
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Dates et versions

hal-00814791 , version 1 (17-04-2013)

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Jan Awrejcewicz, Claude-Henri Lamarque, Kevin A. Broughan. GEOMETRY AND ORDER OF CHAOS. International journal of bifurcation and chaos in applied sciences and engineering , 1999, 9 (2), pp.327-347. ⟨10.1142/S0218127499000201⟩. ⟨hal-00814791⟩

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