Analytic Classification of Families of Linear Differential Systems Unfolding a Resonant Irregular Singularity
We give a complete classification of analytic equivalence of germs of parametric families of systems of complex linear differential equations unfolding a generic resonant singularity of Poincaré rank 1 in dimension n=2 whose leading matrix is a Jordan bloc. The moduli space of analytic equivalence c...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
| ISSN: | 1815-0659 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210604 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Analytic Classification of Families of Linear Differential Systems Unfolding a Resonant Irregular Singularity. Martin Klimeš. SIGMA 16 (2020), 006, 46 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862752783206187008 |
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| author | Klimeš, Martin |
| author_facet | Klimeš, Martin |
| citation_txt | Analytic Classification of Families of Linear Differential Systems Unfolding a Resonant Irregular Singularity. Martin Klimeš. SIGMA 16 (2020), 006, 46 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We give a complete classification of analytic equivalence of germs of parametric families of systems of complex linear differential equations unfolding a generic resonant singularity of Poincaré rank 1 in dimension n=2 whose leading matrix is a Jordan bloc. The moduli space of analytic equivalence classes is described in terms of a tuple of formal invariants and a single analytic invariant obtained from the trace of monodromy, and analytic normal forms are given. We also explain the underlying phenomena of the confluence of two simple singularities and of a turning point, the associated Stokes geometry, and the change of order of Borel summability of formal solutions in dependence on a complex parameter.
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| first_indexed | 2025-12-17T12:04:19Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-210604 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-17T12:04:19Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Klimeš, Martin 2025-12-12T10:39:23Z 2020 Analytic Classification of Families of Linear Differential Systems Unfolding a Resonant Irregular Singularity. Martin Klimeš. SIGMA 16 (2020), 006, 46 pages 1815-0659 2020 Mathematics Subject Classification: 34M03; 34M35; 34M40 arXiv:1301.5228 https://nasplib.isofts.kiev.ua/handle/123456789/210604 https://doi.org/10.3842/SIGMA.2020.006 We give a complete classification of analytic equivalence of germs of parametric families of systems of complex linear differential equations unfolding a generic resonant singularity of Poincaré rank 1 in dimension n=2 whose leading matrix is a Jordan bloc. The moduli space of analytic equivalence classes is described in terms of a tuple of formal invariants and a single analytic invariant obtained from the trace of monodromy, and analytic normal forms are given. We also explain the underlying phenomena of the confluence of two simple singularities and of a turning point, the associated Stokes geometry, and the change of order of Borel summability of formal solutions in dependence on a complex parameter. This article was originally written during my doctoral studies at Université de Montréal under the direction of Christiane Rousseau - I'd like to thank her for her support and encouragement. I'd also like to thank Alexey Glutsyuk and the anonymous referees for their numerous suggestions that helped to improve this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Analytic Classification of Families of Linear Differential Systems Unfolding a Resonant Irregular Singularity Article published earlier |
| spellingShingle | Analytic Classification of Families of Linear Differential Systems Unfolding a Resonant Irregular Singularity Klimeš, Martin |
| title | Analytic Classification of Families of Linear Differential Systems Unfolding a Resonant Irregular Singularity |
| title_full | Analytic Classification of Families of Linear Differential Systems Unfolding a Resonant Irregular Singularity |
| title_fullStr | Analytic Classification of Families of Linear Differential Systems Unfolding a Resonant Irregular Singularity |
| title_full_unstemmed | Analytic Classification of Families of Linear Differential Systems Unfolding a Resonant Irregular Singularity |
| title_short | Analytic Classification of Families of Linear Differential Systems Unfolding a Resonant Irregular Singularity |
| title_sort | analytic classification of families of linear differential systems unfolding a resonant irregular singularity |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210604 |
| work_keys_str_mv | AT klimesmartin analyticclassificationoffamiliesoflineardifferentialsystemsunfoldingaresonantirregularsingularity |