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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm206-0-13,
author = {Ming-Chia Li and Piotr Zgliczy\'nski},
title = {On stability of forcing relations for multidimensional perturbations of interval maps},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {241-251},
zbl = {1187.37059},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm206-0-13}
}
Ming-Chia Li; Piotr Zgliczyński. On stability of forcing relations for multidimensional perturbations of interval maps. Fundamenta Mathematicae, Tome 205 (2009) pp. 241-251. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm206-0-13/