Lorenz Attractors and Generalizations: Geometric and Topological Aspects

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

Manifold 

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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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