Transversality for Critical Relations of Families of Rational Maps: An Elementary Proof

Genadi Levin; Weixiao Shen; Sebastian van Strien

doi:10.1007/978-3-030-16833-9_11

Transversality for Critical Relations of Families of Rational Maps: An Elementary Proof

Genadi Levin, Weixiao Shen, Sebastian van Strien^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Scopus citations

Abstract

In this paper we will give a short and elementary proof that critical relations unfold transversally in the space of rational maps.

Original language	American English
Title of host publication	New Trends in One-Dimensional Dynamics - In Honour of Welington de Melo on the Occasion of His 70th Birthday IMPA 2016
Editors	Maria José Pacifico, Pablo Guarino
Publisher	Springer
Pages	201-220
Number of pages	20
ISBN (Print)	9783030168322
DOIs	https://doi.org/10.1007/978-3-030-16833-9_11
State	Published - 2019
Event	70th Anniversary of Welington de Melo held at IMPA, 2016 - Rio de Janeiro, Brazil Duration: 14 Nov 2016 → 17 Nov 2016

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	285
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	70th Anniversary of Welington de Melo held at IMPA, 2016
Country/Territory	Brazil
City	Rio de Janeiro
Period	14/11/16 → 17/11/16

Bibliographical note

Funding Information:
Acknowledgements The authors thank Alex Eremenko for a discussion about Theorem 2.1,Adam Epstein for pointing out an error in the last paragraph of Sect. 5.1 in a previous version, Xavier Buff and Lasse Rempe-Gillen for helpful comments on the introduction of the final version of this paper and the referee for carefully reading the paper. This project was partly supported by the ISF grant no: 1226/17, ERC AdG grant no: 339523 RGDD and the NSFC grant no: 11731003.

Funding Information:
The authors thank Alex Eremenko for a discussion about Theorem 2.1, Adam Epstein for pointing out an error in the last paragraph of Sect. 5.1 in a previous version, Xavier Buff and Lasse Rempe-Gillen for helpful comments on the introduction of the final version of this paper and the referee for carefully reading the paper. This project was partly supported by the ISF grant no: 1226/17, ERC AdG grant no: 339523 RGDD and the NSFC grant no: 11731003.

Publisher Copyright:
© The Author(s) 2019.

Keywords

Holomorphic dynamics
Rational maps
Transversality

Access to Document

10.1007/978-3-030-16833-9_11

Cite this

Levin, G., Shen, W., & van Strien, S. (2019). Transversality for Critical Relations of Families of Rational Maps: An Elementary Proof. In M. J. Pacifico, & P. Guarino (Eds.), New Trends in One-Dimensional Dynamics - In Honour of Welington de Melo on the Occasion of His 70th Birthday IMPA 2016 (pp. 201-220). (Springer Proceedings in Mathematics and Statistics; Vol. 285). Springer. https://doi.org/10.1007/978-3-030-16833-9_11

Levin, Genadi ; Shen, Weixiao ; van Strien, Sebastian. / Transversality for Critical Relations of Families of Rational Maps : An Elementary Proof. New Trends in One-Dimensional Dynamics - In Honour of Welington de Melo on the Occasion of His 70th Birthday IMPA 2016. editor / Maria José Pacifico ; Pablo Guarino. Springer, 2019. pp. 201-220 (Springer Proceedings in Mathematics and Statistics).

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Levin, G, Shen, W & van Strien, S 2019, Transversality for Critical Relations of Families of Rational Maps: An Elementary Proof. in MJ Pacifico & P Guarino (eds), New Trends in One-Dimensional Dynamics - In Honour of Welington de Melo on the Occasion of His 70th Birthday IMPA 2016. Springer Proceedings in Mathematics and Statistics, vol. 285, Springer, pp. 201-220, 70th Anniversary of Welington de Melo held at IMPA, 2016, Rio de Janeiro, Brazil, 14/11/16. https://doi.org/10.1007/978-3-030-16833-9_11

Transversality for Critical Relations of Families of Rational Maps: An Elementary Proof. / Levin, Genadi; Shen, Weixiao; van Strien, Sebastian.
New Trends in One-Dimensional Dynamics - In Honour of Welington de Melo on the Occasion of His 70th Birthday IMPA 2016. ed. / Maria José Pacifico; Pablo Guarino. Springer, 2019. p. 201-220 (Springer Proceedings in Mathematics and Statistics; Vol. 285).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Levin G, Shen W, van Strien S. Transversality for Critical Relations of Families of Rational Maps: An Elementary Proof. In Pacifico MJ, Guarino P, editors, New Trends in One-Dimensional Dynamics - In Honour of Welington de Melo on the Occasion of His 70th Birthday IMPA 2016. Springer. 2019. p. 201-220. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-030-16833-9_11

Transversality for Critical Relations of Families of Rational Maps: An Elementary Proof

Abstract

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Bibliographical note

Keywords

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