A Case of Monotone Ratio Growth for Quadratic-Like Mappings
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 4, pp. 381-393
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $f_a=-|x|^{\alpha}+a$. Here we treat the
dynamically simplest situation, before the critical point itself
becomes strongly attracting; this corresponds to the kneading
sequence $RRR\ldots, $ or—in the quadratic family—to
the parameters $c\in [-1,0]$ in the Mandelbrot set. We allow the
exponent $\alpha$ to be an arbitrary real number greater than 1.
Keywords:
study monotone parameter behavior ratios consecutive intervals nested family intervals delimited itinerary critical point consider one parameter power law family mappings form alpha here treat dynamically simplest situation before critical point itself becomes strongly attracting corresponds kneading sequence rrr ldots quadratic family parameters mandelbrot set allow exponent alpha arbitrary real number greater
Affiliations des auteurs :
Waldemar Pałuba 1
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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},
pages = {381--393},
publisher = {mathdoc},
volume = {52},
number = {4},
year = {2004},
doi = {10.4064/ba52-4-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ba52-4-4/}
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Waldemar Pałuba. A Case of Monotone Ratio Growth for Quadratic-Like Mappings. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 4, pp. 381-393. doi: 10.4064/ba52-4-4
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