A Self-Similar Dendrite with One-Point Intersection and Infinite Post-Critical Set

Open Access

Original research article

Author(s):

Prabhjot Singh^a, Andrei Tetenov^b

^a Central University of Rajasthan, India
^b Novosibirsk State University, Russia

Advances in the Theory of Nonlinear Analysis and its Applications 2(2), 70-73.

Received: February 12, 2018

Accepted: April 22, 2018

Published: April 25, 2018

Abstract

We build an example of a system S of similarities in R^2 whose attractor is a plane dendrite K⊃[0,1]⊃[0,1] which satisfies one point intersection property, while the post-critical set of the system S is a countable set whose natural projection to K is dense in the middle-third Cantor set.

Keywords: self-similar set, post-critical finiteness, self-similar dendrite, open set condition.

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APA Style

Tetenov, A., & Singh, P. (2018). A self-similar dendrite with one-point intersection and infinite post-critical set. Advances in the Theory of Nonlinear Analysis and its Application, 2(2), 70-73.