Meromorphic first integrals of analytic diffeomorphisms

Armengol Gasull; Xiang Zhang

doi:10.1016/j.jmaa.2022.126796

Meromorphic first integrals of analytic diffeomorphisms

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Resum

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	Anglès
Número d’article	126796
Revista	Journal of Mathematical Analysis and Applications
Volum	519
Número	1
DOIs	https://doi.org/10.1016/j.jmaa.2022.126796
Estat de la publicació	Publicada - 1 de març 2023

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10.1016/j.jmaa.2022.126796

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

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STUDY OF CONTINUOUS AND DISCRETE DYNAMIC SYSTEMS WITH EMPHASIS ON THEIR BIFURCATIONS, PERIODIC ORBITS AND INTEGRABILITY
Llibre Salo, J. (PI), Torregrosa i Arús, J. (Investigador/a Principal 2), Cufi Cabre, C. (Col.laborador/a), Carvalho, Y. R. (Col.laborador/a), Cousillas, G. (Col.laborador/a), Diz Pita, É. (Col.laborador/a), Ferragut Amengual, A. M. (Col.laborador/a), GOUVEIA, L. F. D. S. (Col.laborador/a), Iván Sánchez Sánchez (Col.laborador/a), Jiménez Ruíz, J. J. (Col.laborador/a), RODERO, A. L. (Col.laborador/a), Ramírez, V. (Col.laborador/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. (Col.laborador/a) & Valls Anglés, C. (Col.laborador/a)
1/06/20 → 29/02/24
Projecte: Projectes i Ajuts a la Recerca

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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",

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

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AU - Gasull, Armengol

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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

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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ER -

Meromorphic first integrals of analytic diffeomorphisms

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

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