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17-10-2023

Approximation of Generating Function Barcode for Hamiltonian Diffeomorphisms

Authors: Pazit Haim-Kislev, Ofir Karin

Published in: Foundations of Computational Mathematics | Issue 6/2024

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Abstract

Persistence modules and barcodes are used in symplectic topology to define various invariants of Hamiltonian diffeomorphisms, however numerical methods for computing these barcodes are not yet well developed. In this paper we define one such invariant called the generating function barcode of compactly supported Hamiltonian diffeomorphisms of \( \mathbb {R}^{2n}\) by applying Morse theory to generating functions quadratic at infinity associated to such Hamiltonian diffeomorphisms and provide an algorithm (i.e a finite sequence of explicit calculation steps) that approximates it.

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Metadata
Title
Approximation of Generating Function Barcode for Hamiltonian Diffeomorphisms
Authors
Pazit Haim-Kislev
Ofir Karin
Publication date
17-10-2023
Publisher
Springer US
Published in
Foundations of Computational Mathematics / Issue 6/2024
Print ISSN: 1615-3375
Electronic ISSN: 1615-3383
DOI
https://doi.org/10.1007/s10208-023-09631-w

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