scholarly journals Integrable geodesic flows on tubular sub-manifolds

2018 ◽  
Vol 10 (3-4) ◽  
Author(s):  
Томас Уотерс
Keyword(s):  
Geodesic Flow ◽  
Geodesic Flows ◽  
Jacobi Fields ◽  
3 Dimensional ◽  
New Class ◽  
Integrable Geodesic Flows ◽  
Do So

In this paper we construct a new class of surfaces whose geodesic flow is integrable (in the sense of Liouville). We do so by generalizing the notion of tubes about curves to 3-dimensional manifolds, and using Jacobi fields we derive conditions under which the metric of the generalized tubular sub-manifold admits an ignorable coordinate. Some examples are given, demonstrating that these special surfaces can be quite elaborate and varied.

Expansive geodesic flows on surfaces

1993 ◽  
Vol 13 (1) ◽  
pp. 153-165 ◽  
Author(s):  
Miguel Paternain
Keyword(s):  
Geodesic Flow ◽  
Compact Surface ◽  
Conjugate Points ◽  
Riemannian Surface ◽  
Geodesic Flows ◽  
Flows On Surfaces

AbstractWe prove the following result: if M is a compact Riemannian surface whose geodesic flow is expansive, then M has no conjugate points. This result and the techniques of E. Ghys imply that all expansive geodesic flows of a compact surface are topologically equivalent.

Lord Dufferin and the Indian National Congress, 1885–1888

1967 ◽  
Vol 7 (1) ◽  
pp. 68-96 ◽  
Author(s):  
Briton Martin
Keyword(s):  
Indian Society ◽  
Public Employment ◽  
The Public ◽  
Critical Questions ◽  
New Class ◽  
British Rule ◽  
Growing Body ◽  
National Congress ◽  
The Government ◽  
Do So

In the spring of 1884 shortly before his viceroyalty came to an end, Lord Ripon wrote in an urgent manner to Lord Kimberley, then Secretary of State for India, about one of the more critical questions of policy confronting the Government of India: “You may rely upon it that there are few Indian questions of greater importance in the present day than those which relate to the mode in which we are to deal with the growing body of Natives educated by ourselves in Western learning and Western ideas.” Ripon was pointing to the existence of a new class of English-educated Indians within British-Indian society and to the failure of the Government of India to acknowledge this class and to absorb its talents and influence within the structure of British-Indian administration. That this problem begged for a realistic solution by 1884 and that it would continue to do so in the years ahead, he had no doubts whatsoever; it had been left too long to fester in a mode both damaging to the class itself and dangerous to British rule. In short, the English-educated Indian class had become a question of policy.Simply stated, as the opportunities for Western collegiate education expanded and the avenues leading towards entry into the East India Company's service became available, the doors either failed to open or were placed out of the reach of the educated Indians seeking entry. By 1850, with the new class in existence in limited numbers in Calcutta, Bombay, Madras, and Delhi and with additional graduates appearing annually to swell its ranks, frustrations began to emerge as the graduates found themselves unable to secure the public employment which the Charter Act of 1833 had implied was to be their just right.

Integrable geodesic flows on homogeneous spaces

2001 ◽  
Vol 192 (7) ◽  
pp. 951-968 ◽  
Author(s):  
A V Bolsinov ◽  
B Jovanovic
Keyword(s):  
Homogeneous Spaces ◽  
Geodesic Flows ◽  
Integrable Geodesic Flows

Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards

2019 ◽  
Vol 83 (6) ◽  
pp. 1137-1173 ◽  
Author(s):  
V. V. Vedyushkina (Fokicheva) ◽  
A. T. Fomenko
Keyword(s):  
Geodesic Flows ◽  
Two Dimensional ◽  
Integrable Geodesic Flows

Validity of a Trunk-Mounted Accelerometer to Measure Physical Collisions in Contact Sports

2015 ◽  
Vol 10 (6) ◽  
pp. 681-686 ◽  
Author(s):  
Daniel W.T. Wundersitz ◽  
Paul B. Gastin ◽  
Samuel J. Robertson ◽  
Kevin J. Netto
Keyword(s):  
Effect Size ◽  
Cutoff Frequency ◽  
Triaxial Accelerometer ◽  
Contact Sports ◽  
3 Dimensional ◽  
Acceleration Data ◽  
Impact Acceleration ◽  
Relative Errors ◽  
Tracking Device ◽  
Do So

Context: Accelerometer peak impact accelerations are being used to measure player physical demands in contact sports. However, their accuracy to do so has not been ascertained. Purpose: To compare peak-impact-acceleration data from an accelerometer contained in a wearable tracking device with a 3-dimensional motion-analysis (MA) system during tackling and bumping. Methods: Twenty-five semielite rugby athletes wore a tracking device containing a 100-Hz triaxial accelerometer (MinimaxX S4, Catapult Innovations, Australia). A single retroreflective marker was attached to the device, with its position recorded by a 12-camera MA system during 3 physical-collision tasks (tackle bag, bump pad, and tackle drill; N = 625). The accuracy, effect size, agreement, precision, and relative errors for each comparison were obtained as measures of accelerometer validity. Results: Physical-collision peak impact accelerations recorded by the accelerometer overestimated (mean bias 0.60 g) those recorded by the MA system (P < .01). Filtering the raw data at a 20-Hz cutoff improved the accelerometer’s relationship with MA data (mean bias 0.01 g; P > .05). When considering the data in 9 magnitude bands, the strongest relationship with the MA system was found in the 3.0-g or less band, and the precision of the accelerometer tended to reduce as the magnitude of impact acceleration increased. Of the 3 movements performed, the tackle-bag task displayed the greatest validity with MA. Conclusions: The findings indicate that the MinimaxX S4 accelerometer can accurately measure physical-collision peak impact accelerations when data are filtered at a 20-Hz cutoff frequency. As a result, accelerometers may be useful to measure physical collisions in contact sports.

scholarly journals Approximate solutions of cohomological equations associated with some Anosov flows

1990 ◽  
Vol 10 (2) ◽  
pp. 367-379 ◽  
Author(s):  
Svetlana Katok
Keyword(s):  
Approximate Solutions ◽  
Geodesic Flows ◽  
Curved Surfaces ◽  
Anosov Flow ◽  
3 Dimensional ◽  
Negatively Curved ◽  
Anosov Flows ◽  
Higher Differentiability ◽  
Special Case ◽  
Cohomological Equations

AbstractThe Livshitz theorem reported in 1971 asserts that any C1 function having zero integrals over all periodic orbits of a topologically transitive Anosov flow is a derivative of another C1 function in the direction of the flow. Similar results for functions of higher differentiability have also appeared since. In this paper we prove a ‘finite version’ of the Livshitz theorem for a certain class of Anosov flows on 3-dimensional manifolds which include geodesic flows on negatively curved surfaces as a special case.

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