Asymptotic Behavior of a Surface Implicitly Defined

被引：3
|
作者：
Campo-Montalvo, Elena [1 ]
Fernandez de Sevilla, Marian [1 ]
Perez-Diaz, Sonia [1 ]
机构：
[1] Univ Alcala, Dept Automat, E-28871 Madrid, Spain
来源：
MATHEMATICS | 2022年 / 10卷 / 09期
关键词：
algebraic surfaces implicitly defined; infinity branch; convergent branch; asymptotic behavior; approaching surfaces; TOPOLOGY;
D O I：
10.3390/math10091445
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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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页数：19
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