Piecewise linear iterated function systems on the line of overlapping construction

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چکیده

Abstract In this paper we consider iterated function systems (IFS) on the real line consisting of continuous piecewise linear functions. We assume some bounds contraction ratios functions, but do not any separation condition. Moreover, require that functions IFS are injective, their derivatives separated from zero. prove if fix all slopes perturb other parameters, then for parameters outside an exceptional set less than full packing dimension, Hausdorff dimension attractor is equal to exponent which comes most natural system covers attractor.

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ژورنال

عنوان ژورنال: Nonlinearity

سال: 2021

ISSN: ['0951-7715', '1361-6544']

DOI: https://doi.org/10.1088/1361-6544/ac355e