Continuous-time extensions of discrete-time cocycles Article Swipe
Robin Chemnitz
,
Maximilian Engel
,
Péter Koltai
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1090/bproc/209
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1090/bproc/209
We consider linear cocycles taking values in driven by homeomorphic transformations of a smooth manifold, in discrete and continuous time. We show that any discrete-time cocycle can be extended to a continuous-time cocycle, while preserving its characteristic properties. We provide a necessary and sufficient condition under which this extension is canonical in the sense that the base is extended to an associated suspension flow and that the discrete-time cocycle is recovered as the time-1 map of the continuous-time cocycle. Further, we refine our general result for the case of (quasi-)periodic driving. We use our findings to construct a non-uniformly hyperbolic continuous-time cocycle in over a uniquely ergodic driving.
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- Type
- article
- Language
- lv
- Landing Page
- https://doi.org/10.1090/bproc/209
- https://www.ams.org/bproc/2024-11-03/S2330-1511-2024-00209-9/S2330-1511-2024-00209-9.pdf
- OA Status
- gold
- References
- 15
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4392452502
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W4392452502Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1090/bproc/209Digital Object Identifier
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Continuous-time extensions of discrete-time cocyclesWork title
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articleOpenAlex work type
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lvPrimary language
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2024Year of publication
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2024-03-05Full publication date if available
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Robin Chemnitz, Maximilian Engel, Péter KoltaiList of authors in order
- Landing page
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https://doi.org/10.1090/bproc/209Publisher landing page
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https://www.ams.org/bproc/2024-11-03/S2330-1511-2024-00209-9/S2330-1511-2024-00209-9.pdfDirect link to full text PDF
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YesWhether a free full text is available
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goldOpen access status per OpenAlex
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https://www.ams.org/bproc/2024-11-03/S2330-1511-2024-00209-9/S2330-1511-2024-00209-9.pdfDirect OA link when available
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Discrete time and continuous time, Computer science, Mathematics, StatisticsTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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| abstract_inverted_index.driving. | 137, 204 |
| abstract_inverted_index.extended | 75, 105 |
| abstract_inverted_index.findings | 141 |
| abstract_inverted_index.uniquely | 202 |
| abstract_inverted_index.<mml:math | 9, 152 |
| abstract_inverted_index.<mml:mrow | 28, 39, 171, 178, 185 |
| abstract_inverted_index.Subscript | 17, 160 |
| abstract_inverted_index.canonical | 97 |
| abstract_inverted_index.condition | 91 |
| abstract_inverted_index.construct | 143 |
| abstract_inverted_index.extension | 95 |
| abstract_inverted_index.manifold, | 61 |
| abstract_inverted_index.necessary | 88 |
| abstract_inverted_index.recovered | 117 |
| abstract_inverted_index.<mml:mrow> | 26, 169 |
| abstract_inverted_index.<mml:msub> | 27, 170 |
| abstract_inverted_index.associated | 108 |
| abstract_inverted_index.continuous | 65 |
| abstract_inverted_index.hyperbolic | 146 |
| abstract_inverted_index.preserving | 81 |
| abstract_inverted_index.sufficient | 90 |
| abstract_inverted_index.suspension | 109 |
| abstract_inverted_index.</mml:math> | 52, 198 |
| abstract_inverted_index.</mml:mrow> | 34, 43, 46, 177, 181, 189, 192 |
| abstract_inverted_index.</mml:msub> | 36, 182 |
| abstract_inverted_index.properties. | 84 |
| abstract_inverted_index.homeomorphic | 56 |
| abstract_inverted_index.discrete-time | 71, 114 |
| abstract_inverted_index.double-struck | 21, 164 |
| abstract_inverted_index.non-uniformly | 145 |
| abstract_inverted_index.characteristic | 83 |
| abstract_inverted_index.{SL}_d(\mathbb | 49 |
| abstract_inverted_index.<inline-formula | 7, 150 |
| abstract_inverted_index.<mml:annotation | 47, 193 |
| abstract_inverted_index.<mml:semantics> | 25, 168 |
| abstract_inverted_index.alttext="normal | 11, 154 |
| abstract_inverted_index.continuous-time | 78, 124, 147 |
| abstract_inverted_index.transformations | 57 |
| abstract_inverted_index.(quasi-)periodic | 136 |
| abstract_inverted_index.</mml:semantics> | 51, 197 |
| abstract_inverted_index.left-parenthesis | 20, 163 |
| abstract_inverted_index.{SL}_{2}(\mathbb | 195 |
| abstract_inverted_index.</inline-formula> | 53, 199 |
| abstract_inverted_index.<mml:mi>d</mml:mi> | 35 |
| abstract_inverted_index.<mml:mn>2</mml:mn> | 180 |
| abstract_inverted_index.right-parenthesis"> | 24, 167 |
| abstract_inverted_index.{R})</mml:annotation> | 50, 196 |
| abstract_inverted_index.class="MJX-TeXAtom-ORD"> | 29, 40, 172, 179, 186 |
| abstract_inverted_index.content-type="math/mathml"> | 8, 151 |
| abstract_inverted_index.stretchy="false">(</mml:mo> | 38, 184 |
| abstract_inverted_index.stretchy="false">)</mml:mo> | 45, 191 |
| abstract_inverted_index.mathvariant="normal">L</mml:mi> | 33, 176 |
| abstract_inverted_index.mathvariant="normal">S</mml:mi> | 31, 174 |
| abstract_inverted_index.encoding="application/x-tex">\mathrm | 48, 194 |
| abstract_inverted_index.mathvariant="double-struck">R</mml:mi> | 42, 188 |
| abstract_inverted_index.xmlns:mml="http://www.w3.org/1998/Math/MathML" | 10, 153 |
| cited_by_percentile_year | |
| countries_distinct_count | 2 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile.value | 0.07731915 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |