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On boundaries of attractors in dynamical systems
- Source :
- Communications in Nonlinear Science and Numerical Simulation. 94:105572
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 2021.
-
Abstract
- Fractal geometry is one of the beautiful and challenging branches of mathematics. Self similarity is an important property, exhibited by most of the fractals. Several forms of self similarity have been discussed in the literature. Iterated Function System (IFS) is a mathematical scheme to generate fractals. There are several variants of IFSs such as condensation IFS, countable IFS, etc. In this paper, certain properties of self similar sets, using the concept of boundary are discussed. The notion of boundaries like similarity boundary and dynamical boundary are extended to condensation IFSs. The relationships and measure theoretic properties of boundaries in dynamical systems are analyzed. Self similar sets are characterized using the Hausdorff measure of their boundaries towards the end.
- Subjects :
- Numerical Analysis
Pure mathematics
Self-similarity
Dynamical systems theory
Applied Mathematics
Boundary (topology)
01 natural sciences
Measure (mathematics)
010305 fluids & plasmas
Iterated function system
Fractal
Modeling and Simulation
0103 physical sciences
Attractor
Hausdorff measure
010306 general physics
Mathematics
Subjects
Details
- ISSN :
- 10075704
- Volume :
- 94
- Database :
- OpenAIRE
- Journal :
- Communications in Nonlinear Science and Numerical Simulation
- Accession number :
- edsair.doi...........a3310c28899328878ee24aab7e3b13a5