Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Moscow ; Birmingham
Pleiades Publishing
2005
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| Schriftenreihe: | Proceedings of the Steklov Institute of Mathematics
Volume 249 |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018579115&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | 221 Seiten Illustrationen |
Internformat
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| 100 | 1 | |a Anosov, Dmitrij V. |d 1936-2014 |0 (DE-588)131836153 |4 aut | |
| 245 | 1 | 0 | |a Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings |c D. V. Anosov and E. V. Zhuzhoma |
| 264 | 1 | |a Moscow ; Birmingham |b Pleiades Publishing |c 2005 | |
| 300 | |a 221 Seiten |b Illustrationen | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Proceedings of the Steklov Institute of Mathematics |v Volume 249 | |
| 546 | |a Aus dem Russischen übersetzt | ||
| 700 | 1 | |a Žužoma, Evgenij V. |d 1951- |0 (DE-588)121053547 |4 aut | |
| 830 | 0 | |a Proceedings of the Steklov Institute of Mathematics |v Volume 249 |w (DE-604)BV000009943 |9 249 | |
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Datensatz im Suchindex
| _version_ | 1819266051293052928 |
|---|---|
| adam_text | Titel: Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings
Autor: Anosov, Dmitrij V
Jahr: 2005
Volume 249, 2005
CONTENTS
Introduction...................................................................................... 1
Chapter 1. Basic Definitions and Preliminary Results.................................. 6
1.1. Introductory concepts and notations.............................................. 6
1.1.1. Semi-infinite continuous curves (7). 1.1.2. Universal covering and the absolute (9).
1.1.3. The Frechet distance and the F-equivalence (11). 1.1.4. The limit set of a curve on
a manifold and at infinity (13). 1.1.5. Asymptotic directions and accessible points (15).
1.1.6. Coasymptotic geodesic (16).
1.2. Special families of curves............................................................ 18
1.2.1. Local laminations (18). 1.2.2. Separatrices and generalized leaves (20). 1.2.3. Min-
imal and quasiminimal sets (22). 1.2.4. Closed transversals of local laminations (23).
1.2.5. Geodesic laminations (25). 1.2.6. Flows on surfaces (27).
1.3. Description of points of the absolute.............................................. 28
1.4. Main questions and problems......................................................... 31
Chapter 2. The Anosov and Weil Theorems................................................ 37
2.1. The theorem and conjecture of Weil.............................................. 38
2.1.1. Proof of the Weil theorem (39). 2.1.2. Proof of the Weil conjecture (43). 2.1.3. On
infinite curves on the torus and the Klein bottle (44).
2.2. Anosov theorems on the existence of asymptotic directions.................... 44
2.2.1. Topological flows with a finite number of fixed points (45). 2.2.2. Flows with a con-
tractible set of fixed points (49). 2.2.3. Analytic flows (50).
2.3. Anosov theorems on the approximation of curves by semitrajectories......... 53
2.3.1. Smoothing of compact arcs (54). 2.3.2. Approximation by a smoothly embedded
curve (58). 2.3.3. Proofs of the main theorems (61).
2.4. Example of a curve that cannot be approximated by a leaf of a foliation— 74
Chapter 3. Nonlocal Asymptotic Behavior of Special Curves........................ 89
3.1. Widely disposed curves................................................................ 90
3.2. Semitrajectories of flows............................................................ 93
3.2.1. Nontrivial recurrent semitrajectories (94). 3.2.2. Semitrajectories of analytic and
topological flows with a finite number of fixed points (96). 3.2.3. A generalization of the
Poincare-Bendixson theorem (98).
3.3. Leaves and semileaves of foliations................................................. 99
3.4. Widely disposed local laminations.................................................. 101
3.4.1. Nontrivial recurrent leaves and semileaves (102). 3.4.2. Transversal local lamina-
tions (104). 3.4.3. Invariant manifolds of the points of basic sets (105).
3.5. Geodesic frameworks of local laminations........................................ 106
3.5.1. Geodesic frameworks of quasiminimal sets (107). 3.5.2. Geodesic frameworks of special
foliations (111).
3 6 The image of a geodesic under a covering homeomorphism.......................114
3.7. Curves with constraints imposed on the geodesic curvature.................... 115
Chapter 4. Limit Sets of Curves at Infinity................................................117
4.1. Anosov s wild curve................................................................... 117
4.2. Limit sets of the lifts of curves on the torus.....................................118
Chapter 5. Deviations of Curves from Coasymptotic Geodesics...................... 120
5.1. Unbounded deviation from a geodesic with irrational direction................121
5.1.1. Example of a curve on the torus (121). 5.1.2. The Aranson-Grilles example of a curve
on a hyperbolic surface (124).
5.2. Unbounded deviation from a geodesic with rational direction..................128
5.2.1. The Anosov example (128). 5.2.2. Remote limit points (146). 5.2.3. The Markley-
Vanderschoot example (146).
5.3. Boundedness of deviation of special curves........................................148
5.3.1. Semitrajectories of topological flows on the torus (148). 5.3.2. Semitrajectories of flows
on hyperbolic surfaces (149). 5.3.3. Semitrajectories of analytic flows (154). 5.3.4. Semileaves
of foliations (155). 5.3.5. Invariant manifolds of points of basic sets (155).
5.4. Uniformity of deviations of curves from geodesics............................... 156
Chapter 6. Interplay between the Asymptotic Behavior of Leaves and Their
Properties............................................................................ 158
6.1. The absolute and the dynamical properties of flows............................ 158
6.2. The absolute and the smoothness of flows........................................ 160
6.3. Points of the absolute that are accessible by semitrajectories of flows..... 164
6.4. Oscillation of leaves about coasymptotic geodesics and equidistant curves.. 165
Chapter 7. Applications to Dynamical Systems and Foliations....................... 169
7.1. Classification of irrational flows and foliations................................. 170
7.2. Classification of irrational 2-webs................................................. 181
7.3. Classification of nontrivial minimal sets.......................................... 183
7.4. Classification of homeomorphisms of surfaces with invariant foliations.......185
7.5. Classification of one-dimensional basic sets....................................... 186
7.6. Classification of Cherry flows...................................................... 187
Appendix A. Elements of the Theory of Foliations and Laminations on Surfaces 190
A.l. Examples of foliations and basic definitions......................................... 190
A.l.l. Smoothing topological foliations (191). A.1.2. Index of a singularity and of a
curve (191). A.1.3. Transitive foliations on the disk and sphere (192). A.1.4. Operations
of blowing up a leaf and semileaf (195). A.1.5. Black holes and Rosenberg labyrinths (197).
A.1.6. Denjoy and Cherry foliations (198).
A.2. Poincare-Bendixson theory for local laminations on surfaces................. 199
^ o i ^al?gUeSr7the Cherl7 and Maier theorems (200). A.2.2. Bendixson extension (200).
A.2.3. The list of limit sets of a nonclosed semileaf (203).
A.3. Hyperbolic and Riemannian surfaces .... 203
A.4. Geodesic laminations........................................................................... 206
Appendix B. Certain Facts from Piecewise Linear Topology.. 208
References............................................................................nin
List of conjectures, corollaries, definitions, lemmas, and theorems
Index.............................................
217
219
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| any_adam_object | 1 |
| author | Anosov, Dmitrij V. 1936-2014 Žužoma, Evgenij V. 1951- |
| author_GND | (DE-588)131836153 (DE-588)121053547 |
| author_facet | Anosov, Dmitrij V. 1936-2014 Žužoma, Evgenij V. 1951- |
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| author_sort | Anosov, Dmitrij V. 1936-2014 |
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| series | Proceedings of the Steklov Institute of Mathematics |
| series2 | Proceedings of the Steklov Institute of Mathematics |
| spellingShingle | Anosov, Dmitrij V. 1936-2014 Žužoma, Evgenij V. 1951- Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings Proceedings of the Steklov Institute of Mathematics |
| title | Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings |
| title_auth | Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings |
| title_exact_search | Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings |
| title_full | Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings D. V. Anosov and E. V. Zhuzhoma |
| title_fullStr | Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings D. V. Anosov and E. V. Zhuzhoma |
| title_full_unstemmed | Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings D. V. Anosov and E. V. Zhuzhoma |
| title_short | Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings |
| title_sort | nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018579115&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000009943 |
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