Completion of the classification of generic singularities of geodesic flows in two classes of metrics

N. G. Pavlova; A. O. Remizov

doi:10.1070/im8723

Completion of the classification of generic singularities of geodesic flows in two classes of metrics

Izvestiya Mathematics ◽

10.1070/im8723 ◽

2019 ◽

Vol 83 (1) ◽

pp. 104-123

Author(s):

N. G. Pavlova ◽

A. O. Remizov

Keyword(s):

Geodesic Flows ◽

Generic Singularities

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A complete classification of generic singularities of geodesic flows on 2-surfaces with pseudo-Riemannian metrics

Russian Mathematical Surveys ◽

10.1070/rm9760 ◽

2017 ◽

Vol 72 (3) ◽

pp. 577-579 ◽

Cited By ~ 1

Author(s):

N G Pavlova ◽

A O Remizov

Keyword(s):

Riemannian Metrics ◽

Complete Classification ◽

Geodesic Flows ◽

Generic Singularities

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Liouville Classification of Integrable Geodesic Flows on Two-Dimensional Surface

Integrable Geodesic Flows on Two-Dimensional Surfaces ◽

10.1007/978-1-4615-4307-7_7 ◽

2000 ◽

pp. 167-222

Author(s):

A. V. Bolsinov ◽

A. T. Fomenko

Keyword(s):

Geodesic Flows ◽

Two Dimensional ◽

Integrable Geodesic Flows ◽

Dimensional Surface

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CLASSIFICATION OF GEODESIC FLOWS OF LIOUVILLE METRICS ON THE TWO-DIMENSIONAL TORUS UP TO TOPOLOGICAL EQUIVALENCE

Sbornik Mathematics ◽

10.1070/sm1993v075n02abeh003395 ◽

1993 ◽

Vol 75 (2) ◽

pp. 491-505 ◽

Cited By ~ 2

Author(s):

E N Selivanova

Keyword(s):

Geodesic Flows ◽

Topological Equivalence ◽

Two Dimensional ◽

Dimensional Torus

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Liouville classification of integrable geodesic flows on a torus of revolution in a potential field

Moscow University Mathematics Bulletin ◽

10.3103/s0027132217030056 ◽

2017 ◽

Vol 72 (3) ◽

pp. 121-128 ◽

Cited By ~ 3

Author(s):

D. S. Timonina

Keyword(s):

Potential Field ◽

Geodesic Flows ◽

Integrable Geodesic Flows

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Classification of Generic Singularities for the Planar Time-Optimal Synthesis

SIAM Journal on Control and Optimization ◽

10.1137/s0363012993256149 ◽

1996 ◽

Vol 34 (6) ◽

pp. 1914-1946 ◽

Cited By ~ 40

Author(s):

B. Piccoli

Keyword(s):

Optimal Synthesis ◽

Time Optimal ◽

Generic Singularities

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Topological classification of integrable geodesic flows in a potential field on the torus of revolution

Lobachevskii Journal of Mathematics ◽

10.1134/s1995080217060130 ◽

2017 ◽

Vol 38 (6) ◽

pp. 1108-1120 ◽

Cited By ~ 3

Author(s):

D. S. Timonina

Keyword(s):

Potential Field ◽

Topological Classification ◽

Geodesic Flows ◽

Integrable Geodesic Flows

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Topological Classification of Geodesic Flows on Revolution 2-Surfaces with Potential

Studies in Systems, Decision and Control - Continuous and Distributed Systems II ◽

10.1007/978-3-319-19075-4_2 ◽

2015 ◽

pp. 11-27 ◽

Cited By ~ 4

Author(s):

A. T. Fomenko ◽

E. O. Kantonistova

Keyword(s):

Topological Classification ◽

Geodesic Flows

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Liouville classification of integrable geodesic flows in a potential field on two-dimensional manifolds of revolution: the torus and the Klein bottle

Sbornik Mathematics ◽

10.1070/sm9009 ◽

2018 ◽

Vol 209 (11) ◽

pp. 1644-1676

Author(s):

D. S. Timonina

Keyword(s):

Potential Field ◽

Klein Bottle ◽

Geodesic Flows ◽

Two Dimensional ◽

Integrable Geodesic Flows

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Topological classification of integrable geodesic flows on orientable two-dimensional Riemannian manifolds with additional integral depending on momenta linearly or quadratically

Functional Analysis and Its Applications ◽

10.1007/bf01087536 ◽

1993 ◽

Vol 27 (3) ◽

pp. 186-196 ◽

Cited By ~ 2

Author(s):

Nguen T'en Zung ◽

L. S. Polyakova ◽

E. N. Selivanova

Keyword(s):

Riemannian Manifolds ◽

Topological Classification ◽

Geodesic Flows ◽

Two Dimensional ◽

Integrable Geodesic Flows

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Orbital classification of geodesic flows on two-dimensional ellipsoids. The Jacobi problem is orbitally equivalent to the integrable Euler case in rigid body dynamics

Functional Analysis and Its Applications ◽

10.1007/bf01077048 ◽

1995 ◽

Vol 29 (3) ◽

pp. 149-160 ◽

Cited By ~ 24

Author(s):

A. V. Bolsinov ◽

A. T. Fomenko

Keyword(s):

Rigid Body ◽

Rigid Body Dynamics ◽

Geodesic Flows ◽

Two Dimensional ◽

Body Dynamics

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