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On stability of forcing relations for multidimensional perturbations of interval maps

Ming-Chia Li, Piotr Zgliczyński (2009)

Fundamenta Mathematicae

We show that all periods of periodic points forced by a pattern for interval maps are preserved for high-dimensional maps if the multidimensional perturbation is small. We also show that if an interval map has a fixed point associated with a homoclinic-like orbit then any small multidimensional perturbation has periodic points of all periods.

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