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Journal of Dynamical Systems and Geometric Theories

(Since 2002)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0057·ISSN (Print): 1726-037X

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Half-Yearly Journal: Publishes research on dynamical systems and geometry, including Random Dynamical Systems, hyperbolic behaviour, complex geometry and Ergodic theory.

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Journal of Dynamical Systems and Geometric Theories
Open Access Original Articles

Exceptional Dynamically Invariant Sections

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pp. 141–151Vol. 5Issue 2November 2007DOI: 10.1080/1726037X.2007.10698533XML
Received:
06 Oct 2006
Published Online:
03 Jun 2013
Article type:
Original Articles
Language:
EN
Article no.:
1726037X.2007.10698533
Pages:
141–151

Abstract

In [33] we developed a notion of a Green’s section that generalized the of Green’s currents that arise in higher dimensional holomorphic dynamical systems. In such systems there may be totally invariant currents other than the Green’s currents. These are called exceptional currents. We thus define a corresponding notion of an exceptional section for a continuous self map f : X → X of a topological space X.

Keywords

HolomorphicDynamicsExceptionalHypersurfaceAttracting

References

  1. Briend, Jean-Yves, Cantat, Serge and Shishikura, Mitsuhiro. 2004 . Linearity of the exceptional set for maps of (ℂ) . , 330 ( 1 ) : 39 – 43 .
  2. Briend, Jean-Yves and Duval, Julien. 1999 . Exposants de Liapounoff et distribution des points periodiques d’un endomorphisme de ℂℙ . , 182 ( 2 ) : 143 – 157 .
  3. Briend, Jean-Yves and Duval, Julien. 2001 . Deux caractérisations de la mesure d’équilibre d’un endomorphisme de ı (C) . , : 145 – 159 .
  4. Bedford, Eric and Jonsson, Mattias. 2000 . Dynamics of Regular Polynomial Endomorphisms of ℂ . , 122 : 153 – 212 .
  5. Bedford, Eric, Lyubich, Mikhail and Smillie, John. 1993 . Polynomial diffeomorphisms of ℂ . IV. The measure of maximal entropy and laminar currents . , 112 ( 1 ) : 77 – 125 .
  6. Bredon, Glen E.1997 . , Springer-Verlag .
  7. Bedford, Eric and Smillie, John. 1991 . Polynomial diffeomorphisms of ℂ : currents, equilibrium measure and hyperbolicity . , 103 ( 1 ) : 69 – 99 .
  8. Bedford, Eric and Smillie, John. 1991 . Polynomial diffeomorphisms of ℂ . II. Stable manifolds and recurrence . , 4 ( 4 ) : 657 – 679 .
  9. Bedford, Eric and Smillie, John. 1992 . Polynomial diffeomorphisms of ℂ . III. Ergodicity, exponents and entropy of the equilibrium measure . , 294 ( 3 ) : 395 – 420 .
  10. Bedford, Eric and Smillie, John. 1998 . Polynomial diffeomorphisms of ℂ . V. Critical points and Lyapunov exponents . , 8 ( 3 ) : 349 – 383 .
  11. Bedford, Eric and Smillie, John. 1998 . Polynomial diffeomorphisms of ℂ . VI. Connectivity of . , 148 ( 2 ) : 695 – 735 .
  12. Bedford, Eric and Smillie, John. 1999 . Polynomial diffeomorphisms of ℂ . VII. Hyperbolicity and external rays . , 32 ( 4 ) : 455 – 497 .
  13. Cantat, Serge. 2001 . Dynamique des automorphismes des surfaces 3 . , 187 ( 1 ) : 1 – 57 .
  14. Carleson, Lennart and Gamelin, Theodore W.1993 . , New York: Springer-Verlag .
  15. Douady, A. and Hubbard, J. H.1984–85 . , Orsay: Université de Paris-Sud Département de Mathématique .
  16. Dinh, Tien-Cuong and Sibony, Nessim. 2005 . Green currents for holomorphic automorphisms of compact kähler manifolds . , 18 ( 2 ) : 291 – 312 .
  17. Favre, Charles and Jonsson, Mattias. Preprint.
  18. Favre, Charles and Jonsson, Mattias. 2003 . Brolin’s Theorem for Curves in Two Complex Dimensions . , 53 : 1461 – 1501 .
  19. Friedland, Shmuel and Milnor, John. 1989 . Dynamical properties of plane polynomial automorphisms . , 9 ( 1 ) : 67 – 99 .
  20. Fornaess, John and Sibony, Nessim. 1992 . Complex Henon mappings in ℂ and Fatou-Bieberbach domains . , 65 ( 2 ) : 345 – 380 .
  21. Fornaess, John and Sibony, Nessim. 1994 . “ Complex dynamics in higher dimension ” . In 131 – 186 . In
  22. Fornaess, John and Sibony, Nessim. 1994 . Complex dynamics in higher dimension. I . , 222 : 201 – 231 .
  23. Fornaess, John and Sibony, Nessim. 1995 . “ Complex dynamics in higher dimension ” . In , Vol. II , 135 – 182 . Princeton: Princeton Univ. Press . In
  24. Hartshorne, Robin. 1977 . , Springer-Verlag .
  25. Hubbard, John H. and Oberste-Vorth, Ralph W.1994 . Hénon mappings in the complex domain. I. The global topology of dynamical space . , : 5 – 46 .
  26. Hubbard, John H. and Ralph, Oberste-Vorth W.1995 . “ Hénon mappings in the complex domain. II. Projective and inductive limits of polynomials ” . In , NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci Vol. 464 , 89 – 132 . Dordrecht: Kluwer Acad. Publ . In, of
  27. Hubbard, John H. and Papadopol, Peter. 1994 . Superattractive fixed points in ℂ . , 43 ( 1 ) : 321 – 365 .
  28. McMullen, Curtis T.2002 . Dynamics on 3 surfaces: Salem numbers and Siegel disks . , 545 : 201 – 233 .
  29. Milnor, John. 2006 . , Princeton University Press .
  30. Mane, R., Sad, P. and Sullivan, D.1983 . On the dynamics of rational maps . , 16 ( 2 ) : 193 – 217 .
  31. McMullen, Curtis T. and Sullivan, Dennis P.1998 . Quasiconformal homeomorphisms and dynamics iii. the teichmüller space of a holomorphic dynamical system . , 135 : 351 – 395 .
  32. Robertson, John W.Basic dynamical stability results for ℙ . , To be published.
  33. Robertson, John W.Preprint.
  34. Ueda, Tetsuo. 1994 . Fatou sets in complex dynamics in projective spaces . , 46 : 545 – 555 .
  35. Ueda, Tetsuo. 1998 . Critical orbits of holomorphic maps on projective spaces . , 8 ( 2 ) : 319 – 334 .
  36. Weibel, Charles A.1997 . , Cambridge University Press .
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