On the heteroclinic connection problem for multi-well gradient systems

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:261

Article

Zuniga, Andres¹  Sternberg, Peter¹ 

[1] Indiana Univ, Dept Math, Bloomington, IN 47405 USA

关键词: Heteroclinic orbits;    Multi-well potentials;    Minimizing geodesics;   

DOI  :  10.1016/j.jde.2016.06.010

来源: Elsevier

【 摘 要 】

We revisit the existence problem of heteroclinic connections in RN associated with Hamiltonian systems involving potentials W : R-N -> R having several global minima. Under very mild assumptions on W we present a simple variational approach to first find geodesics minimizing length of curves joining any two of the potential wells, where length is computed with respect to a degenerate metric having conformal factor root W. Then we show that when such a minimizing geodesic avoids passing through other wells of the potential at intermediate times, it gives rise to a heteroclinic connection between the two wells. This work improves upon the approach of [22] and represents a more geometric alternative to the approaches of e.g. [5,10,14,17] for finding such connections. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free