Space of signatures as inverse limits of Carnot groups

Le Donne, Enrico; Züst, Roger (2021). Space of signatures as inverse limits of Carnot groups. ESAIM: COCV, 27(37), p. 37. EDP Sciences 10.1051/cocv/2021040

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We formalize the notion of limit of an inverse system of metric spaces with 1-Lipschitz projections having unbounded fibers. The construction is applied to the sequence of free Carnot groups of fixed rank n and increasing step. In this case, the limit space is in correspondence with the space of signatures of rectifiable paths in R^n, as introduced by Chen. Hambly-Lyons’s result on the uniqueness of signature implies that this space is a geodesic metric tree. As a particular consequence we deduce that every path in R^n can be approximated by projections of some geodesics in some Carnot group of rank n, giving an evidence that the complexity of sub-Riemannian geodesics increases with the step.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Züst, Roger

Subjects:

500 Science > 510 Mathematics

ISSN:

1292-8119

Publisher:

EDP Sciences

Funders:

[UNSPECIFIED] Academy of Finland ; [UNSPECIFIED] Academy of Finland ; [18] European Research Council

Projects:

Projects 288501 not found.
Projects 322989 not found.
Projects 713998 not found.

Language:

English

Submitter:

Sebastiano Don

Date Deposited:

11 Feb 2022 08:01

Last Modified:

05 Dec 2022 16:05

Publisher DOI:

10.1051/cocv/2021040

BORIS DOI:

10.48350/164793

URI:

https://boris.unibe.ch/id/eprint/164793

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