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Lorenz Attractors and Generalizations: Geometric and Topological Aspects

  • Natalia Klinshpont
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 57)

Abstract

In this paper, the problem of topological distinguishing of Lorenz-like attractors and their generalizations is discussed. New cardinal-valued topological invariants for Lorenz-type attractors and generalizations are constructed. A generalization is considered of Williams’s well-known model of the attractor in the Lorenz system, the inverse limit of semiflows on branched manifolds that are suspensions over a discontinuous expanding map of a closed linear interval. The generalization consists in the consideration of maps with several discontinuity points, rather than one. A cardinal-valued topological invariant L-manuscript is constructed that distinguishes a continuum of nonhomeomorphic generalized models. A topological invariant distinguishing a continuum of nonhomeomorphic geometric Lorenz attractors is obtained as a consequence. An analogous cardinal-valued invariant is constructed for attractors of Lorenz-type maps. The kneading invariant is not a topological invariant distinguishing attractors as sets; there exists an uncountable set of mutually nonconjugating Lorenz-type maps having homeomorphic attractors.

Keywords

Unstable Manifold Strange Attractor Lorenz System Inverse Limit Discontinuity Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Obninsk Institute for Nuclear Power EngineeringObninsk, Kaluga RegionRussia

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