engleski

Fractal properties of solutions of differential equations

We give a survey of recent results by the authors and their collaborators concerning fractal analysis of trajectories of dynamical systems, oscillatory solutions of ODE’s and singular sets of weak solutions of elliptic PDE’s. Contents: 1. Introduction, 2. Fractal Properties of Trajectories of Dynamical Systems, 3. Fractal Analysis of Trajectories of Some Schredinger Cauchy Problems, 4. Fractal Oscillations of Second-Order Differential Equations, 5. Nonregularity of Weak Solutions of Elliptic Equations, 6. Fractal Properties of Generalized Fresnel Integrals. Bibliography: 85 references.

box dimension, Minkowski content, spiral, chirp, spiral chirp, multiple spiral, bifurcation, Schr¨odinger equation, Euler equation, Riemann–Weber equation, Hartman– Wintner equation, Bessel equation, half lienar equation, Li´enard equation, Poincar´e map, Hopf bifurcation, weak focus, logistic map, oscillation, fractal oscillatority, clothoid, Fresnel integral, elliptic BVPs, weak solution, nonregularity, singular dimension, Besov space, Sobolev space.

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