Dilatation structures I. FundamentalsMarius 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
E-mail: [email protected]
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.