Ukrainian Mathematical Journal

, Volume 66, Issue 1, pp 42–49 | Cite as

Classification of the Regular Components of Two-Dimensional Inner Maps

  • I. Yu. Vlasenko

We propose a topological classification of dynamical systems generated by two-dimensional inner maps on the fully invariant regular components of a wandering set with special attracting boundary (to within the topological conjugacy).


Jordan Curve Regular Component Invariant Component Reeb Graph Topological Conjugacy 
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  1. 1.
    J. Milnor, Dynamics in One Complex Variable. Introductory Lectures, Vieweg Verlag, Weisbaden (2000).CrossRefzbMATHGoogle Scholar
  2. 2.
    V. V. Sharko, “About Kronrod–Reeb graph of a function on a manifold,” Meth. Funct. Anal. Topol., 12, No. 4, 389–396 (2006).zbMATHMathSciNetGoogle Scholar
  3. 3.
    S. Stoїlow, Leçon sur les Principes Topologiques de la Theorie des Fonctions Analytiques, 2 ed., Gauthier-Villars, Paris (1956).Google Scholar
  4. 4.
    Yu. Yu. Trokhymchuk, “Differentiating, inner mappings, and analyticity criteria,” Proc. Inst. Math., 70 (2008).Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • I. Yu. Vlasenko
    • 1
  1. 1.Institute of Mathematics, Ukrainian National Academy of SciencesKyivUkraine

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