Counterexamples for IFS-attractors |
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| Institution: | 1. Jan Kochanowski University in Kielce, Świetokrzyska 15, Kielce 25–406, Poland;2. University Centre of Defence at the Spanish Air Force Academy, MDE-UPCT, 30720 Santiago de la Ribera, Murcia, Spain;1. School of Computer Science and Engineer, Southeast University, Nanjing 210096, China;2. School of Continuing Education, Southeast University, Nanjing 210096, China;3. School of Computer Engineering, Jiangsu University of Technology, Changzhou, Jiangsu 213001, China;4. School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China;1. School of Science, East China Jiaotong University, Nanchang , Jiangxi, Postal code 330013, PR China;2. School of Mathematics, South China Normal University, Guangzhou, Guangdong, Postal code 510631, PR China;3. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang, Guizhou, Postal code 550001, PR China;1. Guizhou University of Finance and Economics, Guiyang, Guizhou Province, 550000, China;2. China Scientific Institute of Petroleum and Natural Gas Pipelines, Langfang, Hebei Province, 065000, China;3. Southwest Petroleum University, Chengdu, Sichuan Province, 610500, China;1. Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Campus de la Muralla, 30203 Cartagena, Región de Murcia, Spain;2. Departamento de Matemáticas, Universidad de Castilla-La Mancha, Campus de Cuenca, 16071 Cuenca, Spain;3. Department of Mechanical and Industrial Engineering,\nSchool of Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA |
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| Abstract: | In this paper, we deal with the part of Fractal Theory related to finite families of (weak) contractions, called iterated function systems (IFS, herein). An attractor is a compact set which remains invariant for such a family. Thus, we consider spaces homeomorphic to attractors of either IFS or weak IFS, as well, which we will refer to as Banach and topological fractals, respectively. We present a collection of counterexamples in order to show that all the presented definitions are essential, though they are not equivalent in general. |
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