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

Masakazu Onitsuka; Satoshi Tanaka

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

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	43-60
Number of pages	18
Journal	Mathematical Communications
Volume	23
Issue number	1
Publication status	Published - 2018 May
Externally published	Yes

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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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. ",

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N2 - 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.

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

Abstract

Keywords

ASJC Scopus subject areas

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