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

    Blokh, Alexander Oversteegen, Lex Ptacek, Ross and Timorin, Vladlen 2016. Laminations from the main cubioid. Discrete and Continuous Dynamical Systems, Vol. 36, Issue. 9, p. 4665.


    Blokh, Alexander Childers, Doug Levin, Genadi Oversteegen, Lex and Schleicher, Dierk 2016. An extended Fatou–Shishikura inequality and wandering branch continua for polynomials. Advances in Mathematics, Vol. 288, p. 1121.


    BLOKH, ALEXANDER OVERSTEEGEN, LEX PTACEK, ROSS and TIMORIN, VLADLEN 2016. The parameter space of cubic laminations with a fixed critical leaf. Ergodic Theory and Dynamical Systems, p. 1.


    Cui, Guizhen Peng, Wenjuan and Tan, Lei 2016. Renormalizations and Wandering Jordan Curves of Rational Maps. Communications in Mathematical Physics, Vol. 344, Issue. 1, p. 67.


    Levin, Genadi Przytycki, Feliks and Shen, Weixiao 2016. The Lyapunov exponent of holomorphic maps. Inventiones mathematicae, Vol. 205, Issue. 2, p. 363.


    Gao, Yan and Cui, Guizhen 2015. Wandering continua for rational maps. Discrete and Continuous Dynamical Systems, Vol. 36, Issue. 3, p. 1321.


    Blokh, Alexander Oversteegen, Lex Ptacek, Ross and Timorin, Vladlen 2014. The main cubioid. Nonlinearity, Vol. 27, Issue. 8, p. 1879.


    BLOKH, ALEXANDER CURRY, CLINTON and OVERSTEEGEN, LEX 2013. Cubic critical portraits and polynomials with wandering gaps. Ergodic Theory and Dynamical Systems, Vol. 33, Issue. 03, p. 713.


    Blokh, Alexander M. Curry, Clinton P. and Oversteegen, Lex G. 2011. Locally connected models for Julia sets. Advances in Mathematics, Vol. 226, Issue. 2, p. 1621.


    Curry, Clinton P. and Mayer, John C. 2010. Buried points in Julia sets. Journal of Difference Equations and Applications, Vol. 16, Issue. 5-6, p. 435.


    Blokh, Alexander and Oversteegen, Lex 2009. Complex Dynamics.


    PESIN, YA. B. SENTI, S. and ZHANG, K. 2008. Lifting measures to inducing schemes. Ergodic Theory and Dynamical Systems, Vol. 28, Issue. 02,


    Blokh, Alexander and Misiurewicz, Michał 2005. Attractors and recurrence for dendrite-critical polynomials. Journal of Mathematical Analysis and Applications, Vol. 306, Issue. 2, p. 567.


    Yoshida, Masamichi 2005. On the pinched circle model and the absence of wandering domains for a topological polynomial. Indagationes Mathematicae, Vol. 16, Issue. 1, p. 117.


    Blokh, Alexander and Oversteegen, Lex 2004. Wandering triangles exist. Comptes Rendus Mathematique, Vol. 339, Issue. 5, p. 365.


    Kiwi, Jan 2004. Real laminations and the topological dynamics of complex polynomials. Advances in Mathematics, Vol. 184, Issue. 2, p. 207.


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An inequality for laminations, Julia sets and ‘growing trees’

  • A. BLOKH (a1) and G. LEVIN (a2)
  • DOI: http://dx.doi.org/10.1017/S0143385702000032
  • Published online: 01 January 2002
Abstract

For a closed lamination on the unit circle invariant under z\mapsto z^d we prove an inequality relating the number of points in the ‘gaps’ with infinite pairwise disjoint orbits to the degree; in particular, this gives estimates on the cardinality of any such ‘gap’ as well as on the number of distinct grand orbits of such ‘gaps’. As a tool, we introduce and study a dynamically defined growing tree in the quotient space. We also use our techniques to obtain for laminations an analog of Sullivan's no wandering domain theorem. Then we apply these results to Julia sets of polynomials.

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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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