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On the oscillatory integration of some ordinary differential equations

Octavian G. Mustafa (2008)

Archivum Mathematicum

Conditions are given for a class of nonlinear ordinary differential equations x ' ' + a ( t ) w ( x ) = 0 , t t 0 1 , which includes the linear equation to possess solutions x ( t ) with prescribed oblique asymptote that have an oscillatory pseudo-wronskian x ' ( t ) - x ( t ) t .

On the rate of convergence to the neutral attractor of a family of one-dimensional maps

T. Nowicki, M. Sviridenko, G. Świrszcz, S. Winograd (2009)

Fundamenta Mathematicae

For a family of maps f d ( p ) = 1 - ( 1 - p / d ) d , d ∈ [2,∞], p ∈ [0,1]. we analyze the speed of convergence (including constants) to the globally attracting neutral fixed point p = 0. The study is motivated by a problem in the optimization of routing. The aim of this paper is twofold: (1) to extend the usage of dynamical systems to unexplored areas of algorithms and (2) to provide a toolbox for a precise analysis of the iterates near a non-degenerate neutral fixed point.

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