TY - JOUR
T1 - GENERALIZED ITERATED FUNCTION SYSTEMS on HYPERBOLIC NUMBER PLANE
AU - Téllez-Sánchez, Gamaliel Yafte
AU - Bory-Reyes, Juan
N1 - Publisher Copyright:
© 2019 World Scientific Publishing Company.
PY - 2019/6/1
Y1 - 2019/6/1
N2 - Iterated function systems provide the most fundamental framework to create many fascinating fractal sets. They have been extensively studied when the functions are affine transformations of Euclidean spaces. This paper investigates the iterated function systems consisting of affine transformations of the hyperbolic number plane. We show that the basics results of the classical Hutchinson-Barnsley theory can be carried over to construct fractal sets on hyperbolic number plane as its unique fixed point. We also discuss about the notion of hyperbolic derivative of an hyperbolic-valued function and then we use this notion to get some generalization of cookie-cutter Cantor sets in the real line to the hyperbolic number plane.
AB - Iterated function systems provide the most fundamental framework to create many fascinating fractal sets. They have been extensively studied when the functions are affine transformations of Euclidean spaces. This paper investigates the iterated function systems consisting of affine transformations of the hyperbolic number plane. We show that the basics results of the classical Hutchinson-Barnsley theory can be carried over to construct fractal sets on hyperbolic number plane as its unique fixed point. We also discuss about the notion of hyperbolic derivative of an hyperbolic-valued function and then we use this notion to get some generalization of cookie-cutter Cantor sets in the real line to the hyperbolic number plane.
KW - Cookie-Cutter Cantor Sets
KW - Hyperbolic Numbers
KW - Idempotent Representation
KW - Iterated Function System
UR - http://www.scopus.com/inward/record.url?scp=85066080781&partnerID=8YFLogxK
U2 - 10.1142/S0218348X19500452
DO - 10.1142/S0218348X19500452
M3 - Artículo
SN - 0218-348X
VL - 27
JO - Fractals
JF - Fractals
IS - 4
M1 - 1950045
ER -