Box-counting dimension of solution curves for a class of two-dimensional nonautonomous linear differential systems

Masakazu Onitsuka, Satoshi Tanaka

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

The two-dimensional linear differential system x = y, y = −x− h(t)y is considered on [t 0 , ∞), where h ∈ C 1 [t 0 , ∞) and h(t) > 0 for t ≥ t 0 . The box-counting dimension of graphs of solution curves is calculated. Criteria to obtain the box-counting dimension of spirals are also established.

Original languageEnglish
Pages (from-to)43-60
Number of pages18
JournalMathematical Communications
Volume23
Issue number1
Publication statusPublished - 2018 May
Externally publishedYes

Keywords

  • Box-counting dimension
  • Linear system
  • Spiral

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology
  • Applied Mathematics

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