On Some Aspects of the Theory of Anosov Systems: With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2004
|
| Series: | Springer Monographs in Mathematics
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | In this book the seminal 1970 Moscow thesis of Grigoriy A. Margulis is published for the first time. Entitled "On Some Aspects of the Theory of Anosov Systems", it uses ergodic theoretic techniques to study the distribution of periodic orbits of Anosov flows. The thesis introduces the "Margulis measure" and uses it to obtain a precise asymptotic formula for counting periodic orbits. This has an immediate application to counting closed geodesics on negatively curved manifolds. The thesis also contains asymptotic formulas for the number of lattice points on universal coverings of compact manifolds of negative curvature. The thesis is complemented by a survey by Richard Sharp, discussing more recent developments in the theory of periodic orbits for hyperbolic flows, including the results obtained in the light of Dolgopyat's breakthroughs on bounding transfer operators and rates of mixing |
| Physical Description: | 1 Online-Ressource (VII, 144 p) |
| ISBN: | 9783662090701 9783642072642 |
| ISSN: | 1439-7382 |
| DOI: | 10.1007/978-3-662-09070-1 |
Staff View
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV042423418 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s2004 |||| o||u| ||||||eng d | ||
| 020 | |a 9783662090701 |c Online |9 978-3-662-09070-1 | ||
| 020 | |a 9783642072642 |c Print |9 978-3-642-07264-2 | ||
| 024 | 7 | |a 10.1007/978-3-662-09070-1 |2 doi | |
| 035 | |a (OCoLC)863879052 | ||
| 035 | |a (DE-599)BVBBV042423418 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 515.39 |2 23 | |
| 082 | 0 | |a 515.48 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Margulis, Grigoriy A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a On Some Aspects of the Theory of Anosov Systems |b With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows |c by Grigoriy A. Margulis |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 2004 | |
| 300 | |a 1 Online-Ressource (VII, 144 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Springer Monographs in Mathematics |x 1439-7382 | |
| 500 | |a In this book the seminal 1970 Moscow thesis of Grigoriy A. Margulis is published for the first time. Entitled "On Some Aspects of the Theory of Anosov Systems", it uses ergodic theoretic techniques to study the distribution of periodic orbits of Anosov flows. The thesis introduces the "Margulis measure" and uses it to obtain a precise asymptotic formula for counting periodic orbits. This has an immediate application to counting closed geodesics on negatively curved manifolds. The thesis also contains asymptotic formulas for the number of lattice points on universal coverings of compact manifolds of negative curvature. The thesis is complemented by a survey by Richard Sharp, discussing more recent developments in the theory of periodic orbits for hyperbolic flows, including the results obtained in the light of Dolgopyat's breakthroughs on bounding transfer operators and rates of mixing | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Geometry | |
| 650 | 4 | |a Dynamical Systems and Ergodic Theory | |
| 650 | 4 | |a Mathematik | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-662-09070-1 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027858835 | ||
Record in the Search Index
| _version_ | 1804153099123687424 |
|---|---|
| any_adam_object | |
| author | Margulis, Grigoriy A. |
| author_facet | Margulis, Grigoriy A. |
| author_role | aut |
| author_sort | Margulis, Grigoriy A. |
| author_variant | g a m ga gam |
| building | Verbundindex |
| bvnumber | BV042423418 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863879052 (DE-599)BVBBV042423418 |
| dewey-full | 515.39 515.48 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.39 515.48 |
| dewey-search | 515.39 515.48 |
| dewey-sort | 3515.39 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-09070-1 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02372nmm a2200433zc 4500</leader><controlfield tag="001">BV042423418</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s2004 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783662090701</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-662-09070-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642072642</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-642-07264-2</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-662-09070-1</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863879052</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042423418</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.39</subfield><subfield code="2">23</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.48</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Margulis, Grigoriy A.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On Some Aspects of the Theory of Anosov Systems</subfield><subfield code="b">With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows</subfield><subfield code="c">by Grigoriy A. Margulis</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin, Heidelberg</subfield><subfield code="b">Springer Berlin Heidelberg</subfield><subfield code="c">2004</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (VII, 144 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Springer Monographs in Mathematics</subfield><subfield code="x">1439-7382</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">In this book the seminal 1970 Moscow thesis of Grigoriy A. Margulis is published for the first time. Entitled "On Some Aspects of the Theory of Anosov Systems", it uses ergodic theoretic techniques to study the distribution of periodic orbits of Anosov flows. The thesis introduces the "Margulis measure" and uses it to obtain a precise asymptotic formula for counting periodic orbits. This has an immediate application to counting closed geodesics on negatively curved manifolds. The thesis also contains asymptotic formulas for the number of lattice points on universal coverings of compact manifolds of negative curvature. The thesis is complemented by a survey by Richard Sharp, discussing more recent developments in the theory of periodic orbits for hyperbolic flows, including the results obtained in the light of Dolgopyat's breakthroughs on bounding transfer operators and rates of mixing</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differentiable dynamical systems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Dynamical Systems and Ergodic Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-662-09070-1</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027858835</subfield></datafield></record></collection> |
| id | DE-604.BV042423418 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662090701 9783642072642 |
| issn | 1439-7382 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858835 |
| oclc_num | 863879052 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (VII, 144 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Springer Monographs in Mathematics |
| spelling | Margulis, Grigoriy A. Verfasser aut On Some Aspects of the Theory of Anosov Systems With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows by Grigoriy A. Margulis Berlin, Heidelberg Springer Berlin Heidelberg 2004 1 Online-Ressource (VII, 144 p) txt rdacontent c rdamedia cr rdacarrier Springer Monographs in Mathematics 1439-7382 In this book the seminal 1970 Moscow thesis of Grigoriy A. Margulis is published for the first time. Entitled "On Some Aspects of the Theory of Anosov Systems", it uses ergodic theoretic techniques to study the distribution of periodic orbits of Anosov flows. The thesis introduces the "Margulis measure" and uses it to obtain a precise asymptotic formula for counting periodic orbits. This has an immediate application to counting closed geodesics on negatively curved manifolds. The thesis also contains asymptotic formulas for the number of lattice points on universal coverings of compact manifolds of negative curvature. The thesis is complemented by a survey by Richard Sharp, discussing more recent developments in the theory of periodic orbits for hyperbolic flows, including the results obtained in the light of Dolgopyat's breakthroughs on bounding transfer operators and rates of mixing Mathematics Differentiable dynamical systems Geometry Dynamical Systems and Ergodic Theory Mathematik https://doi.org/10.1007/978-3-662-09070-1 Verlag Volltext |
| spellingShingle | Margulis, Grigoriy A. On Some Aspects of the Theory of Anosov Systems With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows Mathematics Differentiable dynamical systems Geometry Dynamical Systems and Ergodic Theory Mathematik |
| title | On Some Aspects of the Theory of Anosov Systems With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows |
| title_auth | On Some Aspects of the Theory of Anosov Systems With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows |
| title_exact_search | On Some Aspects of the Theory of Anosov Systems With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows |
| title_full | On Some Aspects of the Theory of Anosov Systems With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows by Grigoriy A. Margulis |
| title_fullStr | On Some Aspects of the Theory of Anosov Systems With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows by Grigoriy A. Margulis |
| title_full_unstemmed | On Some Aspects of the Theory of Anosov Systems With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows by Grigoriy A. Margulis |
| title_short | On Some Aspects of the Theory of Anosov Systems |
| title_sort | on some aspects of the theory of anosov systems with a survey by richard sharp periodic orbits of hyperbolic flows |
| title_sub | With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows |
| topic | Mathematics Differentiable dynamical systems Geometry Dynamical Systems and Ergodic Theory Mathematik |
| topic_facet | Mathematics Differentiable dynamical systems Geometry Dynamical Systems and Ergodic Theory Mathematik |
| url | https://doi.org/10.1007/978-3-662-09070-1 |
| work_keys_str_mv | AT margulisgrigoriya onsomeaspectsofthetheoryofanosovsystemswithasurveybyrichardsharpperiodicorbitsofhyperbolicflows |