An Index Theorem in Relative K-Theory for First-Order Systems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866912976576970752 |
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| author | Skiba, Robert Strzelecki, Daniel Waterstraat, Nils |
| author_facet | Skiba, Robert Strzelecki, Daniel Waterstraat, Nils |
| contents | Motivated by bifurcation of branches of homoclinic orbits of dynamical systems, we consider families of first-order equations on the real line and introduce a generalisation of previous index theorems by Pejsachowicz, and by Hu and Portaluri. The main novelties of our approach firstly concern the analytical setting, where we lift the common assumption that the equations are asymptotically hyperbolic. Secondly, we consider general compact parameter spaces instead of a single parameter, which results in a remarkably simple index formula in relative $K$-theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_20523 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Index Theorem in Relative K-Theory for First-Order Systems Skiba, Robert Strzelecki, Daniel Waterstraat, Nils Dynamical Systems Functional Analysis K-Theory and Homology 47A53 Motivated by bifurcation of branches of homoclinic orbits of dynamical systems, we consider families of first-order equations on the real line and introduce a generalisation of previous index theorems by Pejsachowicz, and by Hu and Portaluri. The main novelties of our approach firstly concern the analytical setting, where we lift the common assumption that the equations are asymptotically hyperbolic. Secondly, we consider general compact parameter spaces instead of a single parameter, which results in a remarkably simple index formula in relative $K$-theory. |
| title | An Index Theorem in Relative K-Theory for First-Order Systems |
| topic | Dynamical Systems Functional Analysis K-Theory and Homology 47A53 |
| url | https://arxiv.org/abs/2603.20523 |