Rectifiable and nonrectifiable solution curves of half-linear differential systems

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  • Yuki Naito
    Department of Mathematics , Ehime University , Matsuyama , 790-8577 , Japan
  • Mervan Pašić
    Department of Mathematics , Faculty of Electrical Engeneering and Computing, University of Zagreb , 10000 , Zagreb , Croatia
  • Satoshi Tanaka
    Department of Applied Mathematics , Faculty of Science, Okayama University of Science , Okayama , 700-0005 , Japan

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<jats:title>Abstract</jats:title> <jats:p>We study a geometric kind of asymptotic behaviour of every <jats:italic>C</jats:italic> <jats:sup>1</jats:sup> 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.</jats:p>

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