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Volume 30, Issue 4
Painlevé Property and Integrability of Polynomial Dynamical Systems

Wenlei Li & Shaoyun Shi

DOI: 10.13447/j.1674-5647.2014.04.09

Commun. Math. Res., 30 (2014), pp. 358-368.

Published online: 2021-05

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  • Abstract

The main purpose of this paper is to investigate the connection between the Painlevé property and the integrability of polynomial dynamical systems. We show that if a polynomial dynamical system has Painlevé property, then it admits certain class of first integrals. We also present some relationships between the Painlevé property and the structure of the differential Galois group of the corresponding variational equations along some complex integral curve.

  • Keywords

Painlevé property, integrability, differential Galois group

  • AMS Subject Headings

34C14, 37F75, 34M15, 32M25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-30-358, author = {Li , Wenlei and Shi , Shaoyun}, title = {Painlevé Property and Integrability of Polynomial Dynamical Systems}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {30}, number = {4}, pages = {358--368}, abstract = {

The main purpose of this paper is to investigate the connection between the Painlevé property and the integrability of polynomial dynamical systems. We show that if a polynomial dynamical system has Painlevé property, then it admits certain class of first integrals. We also present some relationships between the Painlevé property and the structure of the differential Galois group of the corresponding variational equations along some complex integral curve.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2014.04.09}, url = {http://global-sci.org/intro/article_detail/cmr/18962.html} }
TY - JOUR T1 - Painlevé Property and Integrability of Polynomial Dynamical Systems AU - Li , Wenlei AU - Shi , Shaoyun JO - Communications in Mathematical Research VL - 4 SP - 358 EP - 368 PY - 2021 DA - 2021/05 SN - 30 DO - http://doi.org/10.13447/j.1674-5647.2014.04.09 UR - https://global-sci.org/intro/article_detail/cmr/18962.html KW - Painlevé property, integrability, differential Galois group AB -

The main purpose of this paper is to investigate the connection between the Painlevé property and the integrability of polynomial dynamical systems. We show that if a polynomial dynamical system has Painlevé property, then it admits certain class of first integrals. We also present some relationships between the Painlevé property and the structure of the differential Galois group of the corresponding variational equations along some complex integral curve.

Wenlei Li & Shaoyun Shi. (2021). Painlevé Property and Integrability of Polynomial Dynamical Systems. Communications in Mathematical Research . 30 (4). 358-368. doi:10.13447/j.1674-5647.2014.04.09
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