alexa Dilatation structures I. Fundamentals
ISSN: 1736-4337

Journal of Generalized Lie Theory and Applications
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Research Article

Dilatation structures I. Fundamentals

Marius BULIGA*

”Simion Stoilow” Institute of Mathematics of the Romanian Academy, P.O. BOX 1-764, RO 014700 Bucure¸sti, Romania

*Corresponding Author:
Marius BULIGA
”Simion Stoilow” Institute of Mathematics of the Romanian Academy
P.O. BOX 1-764, RO 014700 Bucure
sti, Romania
E-mail: [email protected]
 

Abstract

A dilatation structure is a concept in between a group and a differential structure. In this article we study fundamental properties of dilatation structures on metric spaces. This is a part of a series of papers which show that such a structure allows to do non-commutative analysis, in the sense of differential calculus, on a large class of metric spaces, some of them fractals. We also describe a formal, universal calculus with binary decorated planar trees, which underlies any dilatation structure.

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