6533b7d0fe1ef96bd125ac46

RESEARCH PRODUCT

Separation properties of (n, m)-IFS attractors

Rinju BaluSunil MathewNicolae Adrian Secelean

subject

Numerical AnalysisApplied Mathematics010102 general mathematicsMathematicsofComputing_NUMERICALANALYSISMinkowski–Bouligand dimensionDimension functionEffective dimension01 natural sciences010101 applied mathematicsCombinatoricsPacking dimensionCollage theoremModeling and SimulationHausdorff dimensionHausdorff measure0101 mathematicsInductive dimensionMathematics

description

Abstract The separation properties of self similar sets are discussed in this article. An open set condition for the (n, m)- iterated function system is introduced and the concepts of self similarity, similarity dimension and Hausdorff dimension of the attractor generated by an (n, m) - iterated function system are studied. It is proved that the similarity dimension and the Hausdorff dimension of the attractor of an (n, m) - iterated function system are equal under this open set condition. Further a necessary and sufficient condition for a set to satisfy the open set condition is established.

yearjournalcountryeditionlanguage
2017-10-01Communications in Nonlinear Science and Numerical Simulation
https://doi.org/10.1016/j.cnsns.2017.04.009