EN
A Self-Similar Dendrite with One-Point Intersection and Infinite Post-Critical Set
Abstract
We build an example of a system S of similarities in R^2 whose attractor is a plane dendrite $K\supset [0,1]$ 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
References
- C. Bandt, N.V. Hung and H. Rao, On the open set condition for self-similar fractals, Proc. Amer. Math. Soc. 134 (2005), 1369-1374
- Charatonik J., Charatonik W., Dendrites, Aportaciones Mat. Comun. 22 (1998), 227-253.
- Hutchinson, J.E. Fractals and self-similarity. Indiana Univ. Math. J 30, 1981, 713-747
- Kigami, J. Analysis on Fractals. Cambridge University Press, 2001
- P.A.P. Moran, Additive functions of intervals and Hausdor measure Proc. Cambridge Philos. Soc. 42 (1946), 15-23
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Publication Date
June 30, 2018
Submission Date
February 12, 2018
Acceptance Date
April 22, 2018
Published in Issue
Year 2018 Volume: 2 Number: 2
APA
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. https://doi.org/10.31197/atnaa.417783
AMA
1.Tetenov A, Singh P. A Self-Similar Dendrite with One-Point Intersection and Infinite Post-Critical Set. ATNAA. 2018;2(2):70-73. doi:10.31197/atnaa.417783
Chicago
Tetenov, Andrei, and Prabhjot Singh. 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. https://doi.org/10.31197/atnaa.417783.
EndNote
Tetenov A, Singh P (June 1, 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.
IEEE
[1]A. Tetenov and P. Singh, “A Self-Similar Dendrite with One-Point Intersection and Infinite Post-Critical Set”, ATNAA, vol. 2, no. 2, pp. 70–73, June 2018, doi: 10.31197/atnaa.417783.
ISNAD
Tetenov, Andrei - Singh, Prabhjot. “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 (June 1, 2018): 70-73. https://doi.org/10.31197/atnaa.417783.
JAMA
1.Tetenov A, Singh P. A Self-Similar Dendrite with One-Point Intersection and Infinite Post-Critical Set. ATNAA. 2018;2:70–73.
MLA
Tetenov, Andrei, and Prabhjot Singh. “A Self-Similar Dendrite With One-Point Intersection and Infinite Post-Critical Set”. Advances in the Theory of Nonlinear Analysis and Its Application, vol. 2, no. 2, June 2018, pp. 70-73, doi:10.31197/atnaa.417783.
Vancouver
1.Andrei Tetenov, Prabhjot Singh. A Self-Similar Dendrite with One-Point Intersection and Infinite Post-Critical Set. ATNAA. 2018 Jun. 1;2(2):70-3. doi:10.31197/atnaa.417783