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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 systems of correspondences on the projective line I: Moduli spaces and multiplier maps
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by Rin Gotou
Conform. Geom. Dyn. 27 (2023), 294-321
DOI: https://doi.org/10.1090/ecgd/387
Published electronically: July 26, 2023

Abstract:

We consider moduli spaces of dynamical systems of correspondences over the projective line as a generalization of moduli spaces of dynamical systems of endomorphisms on the projective line. We define the moduli space $Dyn_{d,e}$ of degree $(d,e)$ correspondences. We construct a family $\rho _c : Dyn_{d,e} \dashrightarrow Dyn_{1,d+e-1}$ of rational maps representation-theoretically. Here we note that $Dyn_{1,d+e-1}$ is identical to the moduli space of the usual dynamical systems of degree $d+e-1$. We show that the moduli space $Dyn_{d,e}$ is rational by using $\rho _c$. Moreover, the multiplier maps for the fixed points factor through $\rho _c$. Furthermore, we show the Woods Hole formulae for correspondences of different degrees are also related by $\rho _c$ and obtain another representation-theoretically simplified form of the formula.
References
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Bibliographic Information
  • Rin Gotou
  • Affiliation: Department of Mathematics, Graduate School of Osaka University, Toyonaka, Osaka 560-0043, Japan
  • MR Author ID: 1514005
  • Email: u661233h@ecs.osaka-u.ac.jp
  • Received by editor(s): September 26, 2021
  • Received by editor(s) in revised form: October 6, 2022, and April 13, 2023
  • Published electronically: July 26, 2023
  • Additional Notes: The author was supported by JSPS KAKENHI Grant-in-Aid for Research Fellow JP202122197.
  • © Copyright 2023 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 27 (2023), 294-321
  • MSC (2020): Primary 37F05; Secondary 12E05, 14C05, 14E08, 37F25, 37P45
  • DOI: https://doi.org/10.1090/ecgd/387
  • MathSciNet review: 4620883