Fractal oscillations of self-adjoint and damped linear differential equations of second-order

DOI10.1016/j.amc.2011.07.047zbMath1244.34052OpenAlexW2021727312MaRDI QIDQ654717

Satoshi Tanaka, Mervan Pašić

Publication date: 29 December 2011

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2011.07.047

zbMATH Keywords

chirpsfractal curvesasymptotic behaviour of solutionsoscillationslinear equationsfractal dimensionBessel equationMinkowski content

Mathematics Subject Classification ID

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Growth and boundedness of solutions to ordinary differential equations (34C11)

Related Items (7)

Oscillatory integrals and fractal dimension ⋮ On initial value problems of fractal delay equations ⋮ Fractal oscillations of chirp functions and applications to second-order linear differential equations ⋮ Estimating the Hausdorff-Besicovitch dimension of boundary of basin of attraction in helicopter trim ⋮ Fractal properties of Bessel functions ⋮ Box-counting dimension of solution curves for a class of two-dimensional nonautonomous linear differential systems ⋮ Box-counting dimension of oscillatory solutions to the Emden-Fowler equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Rectifiable oscillations of self-adjoint and damped linear differential equations of second-order
• Chirp transforms and chirp series
• Rectifiable oscillations in second-order linear differential equations
• The fan-chirp transform for non-stationary harmonic signals
• Wavelet analysis and chirps
• On the chirp decomposition of Weierstrass-Mandelbrot functions, and their time-frequency interpretation.
• Minkowski-Bouligand dimension of solutions of the one-dimensional \(p\)-Laplacian.
• On the partial regularity of energy-minimizing, area-preserving maps
• Detecting highly oscillatory signals by chirplet path pursuit
• Fractal oscillations for a class of second order linear differential equations of Euler type
• Rectifiable and unrectifiable oscillations for a class of second-order linear differential equations of Euler type
• On rectifiable oscillation of Euler type second order linear differential equations
• Generalized Minkowski content, spectrum of fractal drums, fractal strings and the Riemann zeta-function
• On the Minkowski Measurability of Fractals
• Fractal Geometry, Complex Dimensions and Zeta Functions
• Wavelet methods for pointwise regularity and local oscillations of functions

This page was built for publication: Fractal oscillations of self-adjoint and damped linear differential equations of second-order