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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Dynamical properties of families of holomorphic mappings
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by Ratna Pal and Kaushal Verma
Conform. Geom. Dyn. 19 (2015), 323-350
Published electronically: December 10, 2015


We study some dynamical properties of skew products of Hénon maps of $\mathbb {C}^2$ that are fibered over a compact metric space $M$. The problem reduces to understanding the dynamical behavior of the composition of a pseudo-random sequence of Hénon mappings. In analogy with the dynamics of the iterates of a single Hénon map, it is possible to construct fibered Green functions that satisfy suitable invariance properties and the corresponding stable and unstable currents. This analogy is carried forth in two ways: it is shown that the successive pull-backs of a suitable current by the skew Hénon maps converges to a multiple of the fibered stable current and secondly, this convergence result is used to obtain a lower bound on the topological entropy of the skew product in some special cases. The other class of maps that are studied are skew products of holomorphic endomorphisms of $\mathbb {P}^k$ that are again fibered over a compact base. We define the fibered Fatou component and show that they are pseudoconvex and Kobayashi hyperbolic.
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Bibliographic Information
  • Ratna Pal
  • Affiliation: Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India
  • Email:
  • Kaushal Verma
  • Affiliation: Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India
  • MR Author ID: 650937
  • Email:
  • Received by editor(s): April 22, 2015
  • Received by editor(s) in revised form: September 28, 2015
  • Published electronically: December 10, 2015
  • Additional Notes: The first named author was supported by CSIR-UGC (India) fellowship
    The second named author was supported by the DST Swarna Jayanti Fellowship 2009–2010 and a UGC–CAS Grant
  • © Copyright 2015 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 19 (2015), 323-350
  • MSC (2010): Primary 37F45
  • DOI:
  • MathSciNet review: 3440067