A Case of Monotone Ratio Growth for Quadratic-Like Mappings

Waldemar Pałuba. "A Case of Monotone Ratio Growth for Quadratic-Like Mappings." Bulletin of the Polish Academy of Sciences. Mathematics 52.4 (2004): 381-393. <http://eudml.org/doc/280522>.

@article{WaldemarPałuba2004,
abstract = {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 $f_a = -|x|^\{α\} + a$. 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.},
author = {Waldemar Pałuba},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {quadratic-like mapping of an interval; post-critical orbit; Poincaré length; nonlinearity; Poincaré push},
language = {eng},
number = {4},
pages = {381-393},
title = {A Case of Monotone Ratio Growth for Quadratic-Like Mappings},
url = {http://eudml.org/doc/280522},
volume = {52},
year = {2004},
}

TY - JOUR
AU - Waldemar Pałuba
TI - A Case of Monotone Ratio Growth for Quadratic-Like Mappings
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2004
VL - 52
IS - 4
SP - 381
EP - 393
AB - 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 $f_a = -|x|^{α} + a$. 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.
LA - eng
KW - quadratic-like mapping of an interval; post-critical orbit; Poincaré length; nonlinearity; Poincaré push
UR - http://eudml.org/doc/280522
ER -