This is a study of the monotone (in parameter) behavior of the ratios of the consecutive intervals in the nested family of intervals delimited by the itinerary of a critical point. We consider a one-parameter power-law family of mappings of the form . Here we treat the dynamically simplest situation, before the critical point itself becomes strongly attracting; this corresponds to the kneading sequence RRR..., or-in the quadratic family-to the parameters c ∈ [-1,0] in the Mandelbrot set. We allow the exponent α to be an arbitrary real number greater than 1.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-4-4,
author = {Waldemar Pa\l uba},
title = {A Case of Monotone Ratio Growth for Quadratic-Like Mappings},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {52},
year = {2004},
pages = {381-393},
zbl = {1098.37037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-4-4}
}
Waldemar Pałuba. A Case of Monotone Ratio Growth for Quadratic-Like Mappings. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) pp. 381-393. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-4-4/