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Rectifiable and nonrectifiable solution curves of half-linear differential systems

  • Yuki Naito EMAIL logo , Mervan Pašić and Satoshi Tanaka
From the journal Mathematica Slovaca

Abstract

We study a geometric kind of asymptotic behaviour of every C1 solution of a class of nonautonomous systems of half-linear differential equations with continuous coefficients. We give necessary and sufficient conditions such that the image of every solution (solution curve) has finite length (rectifiable curve) and infinite length (nonrectifiable, possible fractal curve). A particular attention is paid to systems having attractive zero solution. The main results are proved by using a new result for the nonrectifiable plane curves.


This work was supported by JSPS KAKENHI Grant Number 26400171 (the first author) and JSPS KAKENHI Grant Number 26400182 (the third author).



Communicated by Michal Fečkan


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Received: 2016-6-3
Accepted: 2017-1-6
Published Online: 2018-5-18
Published in Print: 2018-6-26

© 2018 Mathematical Institute Slovak Academy of Sciences

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