Multiplicity of fixed points and growth of \(\varepsilon \)-neighborhoods of orbits
The multiplicity of a fixed point is studied for nondifferentiable functions along the lines initiated by the third author jointly with \textit{N. Elezović} and \textit{D. Žubrinić} [Chaos Solitons Fractals 34, No. 2, 244--252 (2007; Zbl 1133.37007)] in a differentiable case. The estimation of the multiplicity is this time obtained in a more sophisticated way. More precisely, an appropriate scale is found to which the length of the \(\varepsilon\)-neighbourhood of the close orbits is comparable. Several applications are presented, including those to particular Poincaré maps.
scientific article; zbMATH DE number 6081510
scientific article