6533b837fe1ef96bd12a2673
RESEARCH PRODUCT
On boundaries of attractors in dynamical systems
Nicolae Adrian SeceleanNitha Niralda P CSunil Mathewsubject
Numerical AnalysisPure mathematicsSelf-similarityDynamical systems theoryApplied MathematicsBoundary (topology)01 natural sciencesMeasure (mathematics)010305 fluids & plasmasIterated function systemFractalModeling and Simulation0103 physical sciencesAttractorHausdorff measure010306 general physicsMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-03-01 | Communications in Nonlinear Science and Numerical Simulation |