Transversality in scalar reaction-diffusion equations on a circle

被引：14

作者：

Czaja, Radoslaw ^{[1
,2
]}

Rocha, Carlos ^{[1
]}

机构：

[1] Inst Super Tecn, Dept Matemat, Ctr Anal Matemat Geometria & Sistemas Dinam, P-1049001 Lisbon, Portugal

[2] Silesian Univ, Inst Math, PL-40007 Katowice, Poland

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2008年 / 245卷 / 03期

关键词：

periodic orbit; heteroclinic orbit; transversality; global attractor; zero number;

D O I：

10.1016/j.jde.2008.01.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that stable and unstable manifolds of hyperbolic periodic orbits for general scalar reaction-diffusion equations on a circle always intersect transversally. The argument also shows that for a periodic orbit there are no homoclinic connections. The main tool used in the proofs is Matano's zero number theory dealing with the Sturm nodal properties of the solutions. (c) 2008 Elsevier Inc. All rights reserved.

引用

页码：692 / 721

页数：30

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