Gradient Trajectories For Plane Singular Metrics I: Oscillating Trajectories

Demonstratio mathematica

article

Vincent Grandjean¹ 

[1] Campus do Pici Bloco 914 CEP 60.455-760

关键词: oscillating and non-oscillating trajectories;    singular gradient;    singular metric;   

DOI  :  10.2478/dema-2014-0006

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

In this short note, we construct an example of a real plane analytic singular metric, degenerating only at the origin, such that any gradient trajectory (respectively to this singular metric) of some well chosen function spirals around the origin. The inversion mapping carries this example into an example of a gradient spiraling dynamics at infinity.

【 授权许可】

CC BY