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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2204.02288 |
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| _version_ | 1866912636563619840 |
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| author | Haim-Kislev, Pazit Karin, Ofir |
| author_facet | Haim-Kislev, Pazit Karin, Ofir |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_02288 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Approximation of Generating Function Barcode for Hamiltonian Diffeomorphisms Haim-Kislev, Pazit Karin, Ofir Symplectic Geometry Algebraic Topology 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. |
| title | Approximation of Generating Function Barcode for Hamiltonian Diffeomorphisms |
| topic | Symplectic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2204.02288 |