Asymptotic behavior of a surface implicitly defined

Authors
Campo Montalvo, ElenaUniversity of Alcalá Author; Fernández De Sevilla Vellón, María De Los ÁngelesUniversity of Alcalá Author; Pérez Díaz, SoniaUniversity of Alcalá Author
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/55108
DOI: 10.3390/math10091445
ISSN: 2227-7390
Publisher
MDPI
Date
2022-04-25
Affiliation
Universidad de Alcalá. Departamento de Automática; Universidad de Alcalá. Departamento de Ciencias de la Computación; Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
Funders
Agencia Estatal de Investigación
Bibliographic citation
Campo Montalvo, E., Fernández de Sevilla, M. & Pérez Díaz, S. 2022, "Asymptotic behavior of a surface implicitly defined", Mathematics, vol. 10, no. 9, art. no. 1445.
Keywords
Algebraic surfaces implicitly defined
Infinity branch
Convergent branch
Asymptotic behavior
Approaching surfaces
Project
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113192GB-I00/ES/VISUALIZACION MATEMATICA: FUNDAMENTOS, ALGORITMOS Y APLICACIONES/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/publishedVersion
Publisher's version
https://doi.org/10.3390/math10091445
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Access rights
info:eu-repo/semantics/openAccess
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Abstract
In this paper, we introduce the notion of infinity branches and approaching surfaces. We obtain an algorithm that compares the behavior at the infinity of two given algebraic surfaces that are defined by an irreducible polynomial. Furthermore, we show that if two surfaces have the same asymptotic behavior, the Hausdorff distance between them is finite. All these concepts are new and represent a great advance for the study of surfaces and their applications.
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