# A Case of Monotone Ratio Growth for Quadratic-Like Mappings

Bulletin of the Polish Academy of Sciences. Mathematics (2004)

- Volume: 52, Issue: 4, page 381-393
- ISSN: 0239-7269

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topWaldemar 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 -

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