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Geometry and Dynamics of Automorphisms of \(\mathbb{P}^{2}_\mathbb{C}\)

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

Abstract

In this chapter we study and describe the geometry, dynamics and algebraic classification of the elements in PSL(3, \(\mathbb{C}\)), extending Goldman’s classification for the elements in PU(2, 1) ⊂ PSL(3,\(\mathbb{C}\)). Just as in that case, and more generally for the isometries of manifolds of negative curvature, the automorphisms of \(\mathbb{P}^{2}_\mathbb{C}\) can also be classified into the three types of elliptic, parabolic and loxodromic (or hyperbolic) elements, according to their geometry and dynamics. This classification can be also done algebraically, in terms of their trace.

Keywords

Compact Subset Projective Line Invariant Line Elliptic Element Parabolic Element 
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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