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  • Cited by 2
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Sánchez-Gabites, J. J. 2008. Dynamical systems and shapes. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, Vol. 102, Issue. 1, p. 127.


    Nusse, Helena E. and Yorke, James A. 2007. Bifurcations of basins of attraction from the view point of prime ends. Topology and its Applications, Vol. 154, Issue. 13, p. 2567.


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Characterizing the basins with the most entangled boundaries

  • HELENA E. NUSSE (a1) (a2) and JAMES A. YORKE (a1) (a3)
  • DOI: http://dx.doi.org/10.1017/S0143385702001360
  • Published online: 01 June 2003
Abstract

In dynamical systems examples are common in which two or more attractors coexist and in such cases the basin boundary is non-empty. The purpose of this paper is to describe the structure and properties of basins and their boundaries for two-dimensional diffeomorphisms. If a two-dimensional basin has a basin cell (a trapping region whose boundary consists of pieces of the stable and unstable manifolds of a well-chosen periodic orbit), then the basin consists of a central body (the basin cell) and a finite number of channels attached to it and the basin boundary is fractal. We prove the following surprising property for certain fractal basin boundaries: a basin of attraction B has a basin cell if and only if every diverging path in basin B has the entire basin boundary \partial\bar{B} as its limit set. The latter property reflects a complete entangled basin and its boundary.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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