Self-similar sets satisfying the common point property |
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| Institution: | 1. Indian Institute of Science Education and Research, Kolkata 741246, India;2. Indian Institute of Science Education and Research, Pune 411008, India;3. King Abdulaziz University, Jeddah, Saudi Arabia;1. Faculty of Natural Sciences and Mathematics, University of Maribor, Koro?ak cesta 160, Maribor SI-2000, Slovenia;2. Faculty of Education, University of Maribor, Koro?ak cesta 160, Maribor SI-2000, Slovenia;1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;2. Department of Mathematics, Chongqing Normal University, Chongqing 401331, China;1. Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;2. Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;1. Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Instituto Politécnico Nacional, Av. IPN No. 2580, L. Ticomán, México D.F. 07340, Mexico;2. Petróleos Mexicanos, Av. Prol. de Juárez, Comalcalco, Tabasco 86388, Mexico;3. Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Mexico;4. SATMEX, Av. de las Telecomunicaciones S/N, CONTEL Edif. SGA-II, México, D.F. 09310, Mexico |
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| Abstract: | A self-similar set is a fixed point of iterated function system (IFS) whose maps are similarities. We say that a self-similar set satisfies the common point property if the intersection of images of the attractor under the maps of the IFS is a singleton and this point has a common pre-image, under the maps of the IFS, and the pre-image is in the attractor.Self-similar sets satisfying the common point property were introduced in Sirvent (2008) in the context of space-filling curves. In the present article we study some basic topological and dynamical properties of self-similar sets satisfying the common point property. We show examples of this family of sets.We consider attractors of a sub-IFS, an IFS formed from the original IFS by removing some maps. We put conditions on this attractors for having the common point property, when the original IFS have this property. |
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