Oscillatory and phase dimensions of solutions of some second-order differential equations

DOI10.1016/j.bulsci.2008.03.004zbMath1198.34052OpenAlexW2039766745MaRDI QIDQ1046488

Vesna Županović, Darko Žubrinić, Mervan Pašić

Publication date: 22 December 2009

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2008.03.004

zbMATH Keywords

nonlinear oscillationsbox dimensionLiénard equationnonlinear differential equationchirpspiralweakly damped oscillator

Mathematics Subject Classification ID

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Fractals (28A80) Dimension theory of smooth dynamical systems (37C45)

Related Items

Rectifiability of solutions for a class of two-dimensional linear differential systems, Fractal oscillations of chirp functions and applications to second-order linear differential equations, Fractal properties of Bessel functions, FRACTAL ANALYSIS OF HOPF BIFURCATION AT INFINITY, Box dimension of Neimark–Sacker bifurcation, Box-counting dimension of solution curves for a class of two-dimensional nonautonomous linear differential systems

Cites Work

• Rectifiable oscillations in second-order half-linear differential equations
• Analysis of Minkowski contents of fractal sets and applications
• The period function of classical Liénard equations
• Rectifiable oscillations in second-order linear differential equations
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• Minkowski-Bouligand dimension of solutions of the one-dimensional \(p\)-Laplacian.
• Fractal analysis of spiral trajectories of some planar vector fields
• Generalized Liénard equations, cyclicity and Hopf-Takens bifurcations
• Box dimension of trajectories of some discrete dynamical systems
• Fractal oscillations for a class of second order linear differential equations of Euler type
• Qualitative theory of planar differential systems
• Fractal analysis of spiral trajectories of some vector fields in \(\mathbb R^3\)
• Poincaré map in fractal analysis of spiral trajectories of planar vector fields
• Rectifiable and unrectifiable oscillations for a class of second-order linear differential equations of Euler type
• More limit cycles than expected in Liénard equations
• On rectifiable oscillation of Euler type second order linear differential equations
• Wavelet methods for pointwise regularity and local oscillations of functions
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