Escape of mass and entropy for diagonal flows in real rank one situations Article Swipe
Manfred Einsiedler
,
Shirali Kadyrov
,
Anke Pohl
·
YOU?
·
· 2015
· Open Access
·
· DOI: https://doi.org/10.3929/ethz-b-000106381
YOU?
·
· 2015
· Open Access
·
· DOI: https://doi.org/10.3929/ethz-b-000106381
Let $G$ be a connected semisimple Lie group of real rank 1 with finite center, let $Γ$ be a non-uniform lattice in $G$ and $a$ any diagonalizable element in $G$. We investigate the relation between the metric entropy of $a$ acting on the homogeneous space $Γ\backslash G$ and escape of mass. Moreover, we provide bounds on the escaping mass and, as an application, we show that the Hausdorff dimension of the set of orbits (under iteration of $a$) which miss a fixed open set is not full.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1110.0910
- https://arxiv.org/pdf/1110.0910
- OA Status
- green
- Cited By
- 3
- References
- 14
- Related Works
- 20
- OpenAlex ID
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https://openalex.org/W2949991502Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.3929/ethz-b-000106381Digital Object Identifier
- Title
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Escape of mass and entropy for diagonal flows in real rank one situationsWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2015Year of publication
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2015-01-01Full publication date if available
- Authors
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Manfred Einsiedler, Shirali Kadyrov, Anke PohlList of authors in order
- Landing page
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https://arxiv.org/abs/1110.0910Publisher landing page
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https://arxiv.org/pdf/1110.0910Direct link to full text PDF
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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- Concepts
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Mathematics, Backslash, Diagonalizable matrix, Hausdorff dimension, Diagonal, Entropy (arrow of time), Rank (graph theory), Pure mathematics, Combinatorics, Physics, Geometry, Symmetric matrix, Quantum mechanics, Eigenvalues and eigenvectorsTop concepts (fields/topics) attached by OpenAlex
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3Total citation count in OpenAlex
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2018: 1, 2015: 1, 2013: 1Per-year citation counts (last 5 years)
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20Other works algorithmically related by OpenAlex
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| best_oa_location.landing_page_url | http://arxiv.org/abs/1110.0910 |
| primary_location.id | pmh:oai:arXiv.org:1110.0910 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4306400194 |
| primary_location.source.issn | |
| primary_location.source.type | repository |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | |
| primary_location.source.is_core | False |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | arXiv (Cornell University) |
| primary_location.source.host_organization | https://openalex.org/I205783295 |
| primary_location.source.host_organization_name | Cornell University |
| primary_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| primary_location.license | |
| primary_location.pdf_url | https://arxiv.org/pdf/1110.0910 |
| primary_location.version | submittedVersion |
| primary_location.raw_type | text |
| primary_location.license_id | |
| primary_location.is_accepted | False |
| primary_location.is_published | False |
| primary_location.raw_source_name | |
| primary_location.landing_page_url | http://arxiv.org/abs/1110.0910 |
| publication_date | 2015-01-01 |
| publication_year | 2015 |
| referenced_works | https://openalex.org/W2951657989, https://openalex.org/W3106092138, https://openalex.org/W2330758374, https://openalex.org/W1487391391, https://openalex.org/W2045017310, https://openalex.org/W2063764685, https://openalex.org/W2964329865, https://openalex.org/W2015209433, https://openalex.org/W1527329021, https://openalex.org/W1983894121, https://openalex.org/W2142097987, https://openalex.org/W2169687370, https://openalex.org/W2088544526, https://openalex.org/W2963860365 |
| referenced_works_count | 14 |
| abstract_inverted_index.1 | 11 |
| abstract_inverted_index.a | 3, 18, 80 |
| abstract_inverted_index.G$ | 46 |
| abstract_inverted_index.We | 30 |
| abstract_inverted_index.an | 61 |
| abstract_inverted_index.as | 60 |
| abstract_inverted_index.be | 2, 17 |
| abstract_inverted_index.in | 21, 28 |
| abstract_inverted_index.is | 84 |
| abstract_inverted_index.of | 8, 38, 49, 69, 72, 76 |
| abstract_inverted_index.on | 41, 55 |
| abstract_inverted_index.we | 52, 63 |
| abstract_inverted_index.$G$ | 1, 22 |
| abstract_inverted_index.$a$ | 24, 39 |
| abstract_inverted_index.Let | 0 |
| abstract_inverted_index.Lie | 6 |
| abstract_inverted_index.and | 23, 47 |
| abstract_inverted_index.any | 25 |
| abstract_inverted_index.let | 15 |
| abstract_inverted_index.not | 85 |
| abstract_inverted_index.set | 71, 83 |
| abstract_inverted_index.the | 32, 35, 42, 56, 66, 70 |
| abstract_inverted_index.$G$. | 29 |
| abstract_inverted_index.$a$) | 77 |
| abstract_inverted_index.$Γ$ | 16 |
| abstract_inverted_index.and, | 59 |
| abstract_inverted_index.mass | 58 |
| abstract_inverted_index.miss | 79 |
| abstract_inverted_index.open | 82 |
| abstract_inverted_index.rank | 10 |
| abstract_inverted_index.real | 9 |
| abstract_inverted_index.show | 64 |
| abstract_inverted_index.that | 65 |
| abstract_inverted_index.with | 12 |
| abstract_inverted_index.fixed | 81 |
| abstract_inverted_index.full. | 86 |
| abstract_inverted_index.group | 7 |
| abstract_inverted_index.mass. | 50 |
| abstract_inverted_index.space | 44 |
| abstract_inverted_index.which | 78 |
| abstract_inverted_index.(under | 74 |
| abstract_inverted_index.acting | 40 |
| abstract_inverted_index.bounds | 54 |
| abstract_inverted_index.escape | 48 |
| abstract_inverted_index.finite | 13 |
| abstract_inverted_index.metric | 36 |
| abstract_inverted_index.orbits | 73 |
| abstract_inverted_index.between | 34 |
| abstract_inverted_index.center, | 14 |
| abstract_inverted_index.element | 27 |
| abstract_inverted_index.entropy | 37 |
| abstract_inverted_index.lattice | 20 |
| abstract_inverted_index.provide | 53 |
| abstract_inverted_index.escaping | 57 |
| abstract_inverted_index.relation | 33 |
| abstract_inverted_index.Hausdorff | 67 |
| abstract_inverted_index.Moreover, | 51 |
| abstract_inverted_index.connected | 4 |
| abstract_inverted_index.dimension | 68 |
| abstract_inverted_index.iteration | 75 |
| abstract_inverted_index.semisimple | 5 |
| abstract_inverted_index.homogeneous | 43 |
| abstract_inverted_index.investigate | 31 |
| abstract_inverted_index.non-uniform | 19 |
| abstract_inverted_index.application, | 62 |
| abstract_inverted_index.$Γ\backslash | 45 |
| abstract_inverted_index.diagonalizable | 26 |
| cited_by_percentile_year.max | 94 |
| cited_by_percentile_year.min | 89 |
| countries_distinct_count | 3 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile.value | 0.80686538 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |