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The Limit Set in Dimension 2

  • Angel Cano
  • Juan Pablo Navarrete
  • José Seade
Chapter
Part of the Progress in Mathematics book series (PM, volume 303)

Abstract

As we know already, there is no unique notion of “the limit set” for complex Kleinian groups in higher dimensions. There are instead several natural such notions, each with its own properties and characteristics, providing each a different kind of information about the geometry and dynamics of the group. The Kulkarni limit set has the property of “quasi-minimality”, which is interesting for understanding the minimal invariant sets; and the action on its complement is properly discontinuous, which is useful for studying geometric properties of the group. Yet, this may not be the largest region where the action is properly discontinuous. There is also the region of equicontinuity, which provides a set where we can use the powerful tools of analysis to study the group action.

Keywords

General Position Projective Line Kleinian Group Riemann Sphere Iteration Theory 
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 Basel 2013

Authors and Affiliations

  • Angel Cano
    • 1
  • Juan Pablo Navarrete
    • 2
  • José Seade
    • 1
  1. 1.Instituto de MatemáticasUniversidad Nacional Autónoma de México Unidad CuernavacaCuernavacaMexico
  2. 2.Facultad de MatemáticasUniversidad Autónoma de YucatánMéridaMexico

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