Articles liés à Fractal Space: Introduction and Applications

Fractal Space: Introduction and Applications - Couverture souple

S. Nair, Minirani; Mathew, Sunil

 
9783659808241: Fractal Space: Introduction and Applications
Couverture souple
ISBN 10 : 3659808245 ISBN 13 : 9783659808241
Editeur : LAP LAMBERT Academic Publishing, 2015

Synopsis

Fractal Geometry was developed to understand the geometry of irregular sets which was not possible using methods from classical Euclidean geometry. The setting of a similitude Iterated Function System (IFS) has provided a sufficiently easy environment to produce highly irregular sets which are fractals. In this book, the notion of scaled IFS is defined and its existence conditions are examined. A lower and upper bounds for the Hausdorff dimension of the attractor of a scaled IFS is obtained. We have explained the construction of some super self similar sets. The topology induced by Hausdorff metric on the set of all non empty compact subsets of a complete metric space is explained. The relation between this topology and the convergence of sets is discussed. Partial metric space is the generalization of a metric space with non zero self distance. The completeness of the space under Hausdorff partial metric is proved and the definitions of fractals is extended to this metric space. Some applications of the field of study in the area of ocean sciences are discussed.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

Fractal Geometry was developed to understand the geometry of irregular sets which was not possible using methods from classical Euclidean geometry. The setting of a similitude Iterated Function System (IFS) has provided a sufficiently easy environment to produce highly irregular sets which are fractals. In this book, the notion of scaled IFS is defined and its existence conditions are examined. A lower and upper bounds for the Hausdorff dimension of the attractor of a scaled IFS is obtained. We have explained the construction of some super self similar sets. The topology induced by Hausdorff metric on the set of all non empty compact subsets of a complete metric space is explained. The relation between this topology and the convergence of sets is discussed. Partial metric space is the generalization of a metric space with non zero self distance. The completeness of the space under Hausdorff partial metric is proved and the definitions of fractals is extended to this metric space. Some applications of the field of study in the area of ocean sciences are discussed.

Biographie de l'auteur

Dr. Minirani S is an Assistant Professor in Mathematics at Don Bosco Institute of Technology, Mumbai, India. She has done her Masters in Mathematics from the University of Calicut and PhD from National Institute of Technology, Calicut, India. Her areas of interests include Fractal Geometry, Complex Dynamics and Graph Theory.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2015
Langue
anglais
ISBN 10 
3659808245
ISBN 13 
9783659808241
Reliure
Broché
Nombre de pages
68
Coordonnées du fabricant
non disponible
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