Meromorphic first integrals of analytic diffeomorphisms

Armengol Gasull; Xiang Zhang

doi:10.1016/j.jmaa.2022.126796

Meromorphic first integrals of analytic diffeomorphisms

Armengol Gasull, Xiang Zhang

Producción científica: Contribución a una revista › Artículo › Investigación › revisión exhaustiva

1 Cita (Scopus)

Resumen

We give an upper bound for the number of functionally independent meromorphic first integrals that a discrete dynamical system generated by an analytic map f can have in a neighborhood of one of its fixed points. This bound is obtained in terms of the resonances among the eigenvalues of the differential of f at this point. Our approach is inspired on similar Poincaré type results for ordinary differential equations. We also apply our results to several examples, some of them motivated by the study of several difference equations.

Idioma original	Inglés
Número de artículo	126796
Publicación	Journal of Mathematical Analysis and Applications
Volumen	519
N.º	1
DOI	https://doi.org/10.1016/j.jmaa.2022.126796
Estado	Publicada - 1 mar 2023

Acceder al documento

10.1016/j.jmaa.2022.126796

https://ddd.uab.cat/record/267129

Otros archivos y enlaces

STUDY OF CONTINUOUS AND DISCRETE DYNAMIC SYSTEMS WITH EMPHASIS ON THEIR BIFURCATIONS, PERIODIC ORBITS AND INTEGRABILITY
Llibre Salo, J. (Principal Investigator), Torregrosa i Arús, J. (Co-Investigador/a Principal), Cufi Cabre, C. (Colaborador/a), Carvalho, Y. R. (Colaborador/a), Cousillas, G. (Colaborador/a), Diz Pita, É. (Colaborador/a), Ferragut Amengual, A. M. (Colaborador/a), GOUVEIA, L. F. D. S. (Colaborador/a), Iván Sánchez Sánchez (Colaborador/a), Jiménez Ruíz, J. J. (Colaborador/a), RODERO, A. L. (Colaborador/a), Ramírez, V. (Colaborador/a), Artes Ferragud, J. C. (Investigador/a), Caubergh , M. M. (Investigador/a), Cima Mollet, A. M. (Investigador/a), Corbera Subirana, M. (Investigador/a), Cors Iglesias, J. M. (Investigador/a), Gasull Embid, A. (Investigador/a), Pantazi ., C. (Investigador/a), Soler Villanueva, J. (Investigador/a), Garrido Pelaez, J. M. (Colaborador/a) & Valls Anglés, C. (Colaborador/a)
1/06/20 → 29/02/24
Proyecto: Proyectos y Ayudas de Investigación

Citar esto

@article{227cce6e1dff46d89d79910bd7ac62d2,

title = "Meromorphic first integrals of analytic diffeomorphisms",

abstract = "We give an upper bound for the number of functionally independent meromorphic first integrals that a discrete dynamical system generated by an analytic map f can have in a neighborhood of one of its fixed points. This bound is obtained in terms of the resonances among the eigenvalues of the differential of f at this point. Our approach is inspired on similar Poincar{\'e} type results for ordinary differential equations. We also apply our results to several examples, some of them motivated by the study of several difference equations.",

keywords = "Discrete dynamical system, Integrability, Meromorphic first integrals",

author = "Armengol Gasull and Xiang Zhang",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",

year = "2023",

month = mar,

day = "1",

doi = "10.1016/j.jmaa.2022.126796",

language = "English",

volume = "519",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Meromorphic first integrals of analytic diffeomorphisms

AU - Gasull, Armengol

AU - Zhang, Xiang

PY - 2023/3/1

Y1 - 2023/3/1

N2 - We give an upper bound for the number of functionally independent meromorphic first integrals that a discrete dynamical system generated by an analytic map f can have in a neighborhood of one of its fixed points. This bound is obtained in terms of the resonances among the eigenvalues of the differential of f at this point. Our approach is inspired on similar Poincaré type results for ordinary differential equations. We also apply our results to several examples, some of them motivated by the study of several difference equations.

AB - We give an upper bound for the number of functionally independent meromorphic first integrals that a discrete dynamical system generated by an analytic map f can have in a neighborhood of one of its fixed points. This bound is obtained in terms of the resonances among the eigenvalues of the differential of f at this point. Our approach is inspired on similar Poincaré type results for ordinary differential equations. We also apply our results to several examples, some of them motivated by the study of several difference equations.

KW - Discrete dynamical system

KW - Integrability

KW - Meromorphic first integrals

UR - http://www.scopus.com/inward/record.url?scp=85140455366&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/a4075595-9ba7-38f5-a99c-d635df95681d/

U2 - 10.1016/j.jmaa.2022.126796

DO - 10.1016/j.jmaa.2022.126796

M3 - Article

SN - 0022-247X

VL - 519

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

M1 - 126796

ER -

Meromorphic first integrals of analytic diffeomorphisms

Resumen

Acceder al documento

Otros archivos y enlaces

Huella

Proyectos

STUDY OF CONTINUOUS AND DISCRETE DYNAMIC SYSTEMS WITH EMPHASIS ON THEIR BIFURCATIONS, PERIODIC ORBITS AND INTEGRABILITY

Citar esto