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Mathematics > Dynamical Systems
Title: On planar curves with position-dependent curvature
(Submitted on 16 Jul 2021 (v1), last revised 21 Apr 2022 (this version, v4))
Abstract: Motivated by homothetic solutions to curvature-driven flows of planar curves, as well as their many physical applications, this work carries out a systematic study of oriented curves whose curvature $\kappa$ is a given function of position or direction. The analysis is informed by a dynamical systems point of view. Though focussed on situations where the prescribed curvature depends only on the distance $r$ from a distinguished point, the basic dynamical concepts are seen to apply in other situations as well. As an application, a complete classification of all simple closed solutions of $\kappa = ar^b$, with real constants $a,b$, is established.
Submission history
From: Arno Berger [view email][v1] Fri, 16 Jul 2021 02:59:11 GMT (372kb)
[v2] Sat, 24 Jul 2021 20:26:09 GMT (371kb)
[v3] Mon, 11 Apr 2022 01:28:30 GMT (371kb)
[v4] Thu, 21 Apr 2022 22:18:36 GMT (371kb)
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