Elisabeth Burroni | Searcharxiv

arXiv2013

In the heart of representable metric jets

Here, I aim to immerse myself in the heart of the metric jets, more precisely of those which are representable, restricting myself to the main basic concepts, while going deeper into some notions already mentionned in our previous papers; this will give me the opportunity of lightening the previous texts (including some proofs), while precising some ideas and giving new examples (as the bifractal wave function) with a proof at the end of this paper. Concerning the concrete examples found all along this paper: they play the "starring role" in the understanding of our metric Differential Calculus!

math.CT↗

arXiv2009

Elements for a metric tangential calculus

The metric jets, introduced in the first chapter, generalize the jets (at order one) of Charles Ehresmann. In short, for a "good" map $f$ (said to be "tangentiable" at $a$), we define its metric jet tangent at $a$ (composed of all the maps which are locally lipschitzian at $a$ and tangent to $f$ at $a$) called the "tangential" of $f$ at $a$, and denoted T$f_a$ (the domain and codomain of $f$ being metric spaces). Furthermore, guided by the heuristic example of the metric jet T$f_a$, tangent to a map $f$ differentiable at $a$, which can be canonically represented by the unique continuous affine map it contains, we will extend, in the second chapter, into a specific metric context, this property of representation of a metric jet.This yields a lot of relevant examples of such representations.

math.CT↗