A Case of Monotone Ratio Growth for Quadratic-Like Mappings

• Autorzy: Waldemar Pałuba
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: 52
• Numer: 4
• Strony: 381-393

Daty

wydano

2004

Twórcy

autor

Waldemar Pałuba

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba52-4-4