Singular Lagrangian manifolds and their Lagrangian maps

1990 ◽  
Vol 52 (4) ◽  
pp. 3246-3278 ◽  
Author(s):  
A. B. Givental'
Keyword(s):  
Lagrangian Maps ◽  
Lagrangian Manifolds

scholarly journals Degenerations of invariant Lagrangian manifolds

2014 ◽  
Author(s):  
Mauricio Garay
Keyword(s):  
Lagrangian Manifolds

Complex Lagrangian Manifolds

1990 ◽  
pp. 116-179
Author(s):  
A. S. Mishchenko ◽  
V. E. Shatalov ◽  
B. Yu. Sternin
Keyword(s):  
Lagrangian Manifolds

Construction of invariant measures of Lagrangian maps: minimisation and relaxation

2001 ◽  
Vol 237 (3) ◽  
pp. 469-504
Author(s):  
Siniša Slijepčevič
Keyword(s):  
Invariant Measures ◽  
Lagrangian Maps

Chattering regimes and Lagrangian manifolds in problems with phase constraints

2012 ◽  
Vol 76 (1) ◽  
pp. 1-38
Author(s):  
Vladimir F Borisov ◽  
Vladimir V Gael' ◽  
Mikhail I Zelikin
Keyword(s):  
Phase Constraints ◽  
Lagrangian Manifolds

Parallelism of distributions and geodesics on F(2K + S; S)-structure Lagrangian manifolds

2014 ◽  
Vol 9 ◽  
pp. 515-522
Author(s):  
Abhishek Singh ◽  
Ramesh Kumar Pandey ◽  
Sachin Khare
Keyword(s):  
Lagrangian Manifolds

Synoptic Lagrangian maps: Application to surface transport in Monterey Bay

2006 ◽  
Vol 64 (2) ◽  
pp. 221-247 ◽  
Author(s):  
B. L. Lipphardt ◽  
D. Small ◽  
A. D. Kirwan ◽  
S. Wiggins ◽  
K. Ide ◽  
...  
Keyword(s):  
Monterey Bay ◽  
Surface Transport ◽  
Lagrangian Maps

Canonical Maslov operator on Lagrangian manifolds with Hilbert model

1990 ◽  
Vol 48 (6) ◽  
pp. 1206-1213 ◽  
Author(s):  
A. Yu. Daletskii
Keyword(s):  
Canonical Maslov Operator ◽  
Lagrangian Manifolds ◽  
Maslov Operator

Equivariant Singularities of Lagrangian Manifolds and Uniaxial Ferromagnet

1987 ◽  
Vol 47 (6) ◽  
pp. 1342-1360 ◽  
Author(s):  
Stanislaw Janeczko ◽  
Adam Kowalczyk
Keyword(s):  
Uniaxial Ferromagnet ◽  
Lagrangian Manifolds

scholarly journals The biogeochemical structuring role of horizontal stirring: Lagrangian perspectives on iron delivery downstream of the Kerguelen plateau

2015 ◽  
Vol 12 (1) ◽  
pp. 779-814 ◽  
Author(s):  
F. d'Ovidio ◽  
A. Della Penna ◽  
T. W. Trull ◽  
F. Nencioli ◽  
I. Pujol ◽  
...  
Keyword(s):  
Adaptive Sampling ◽  
Sampling Strategy ◽  
Ground Truth ◽  
Global Ocean ◽  
Back Trajectories ◽  
Iron Supply ◽  
Lagrangian Maps ◽  
The One ◽  
Iron Delivery

Abstract. Field campaigns are instrumental in providing ground truth for understanding and modelling global ocean biogeochemical budgets. A survey however can only inspect a fraction of the global oceans, typically a region 100s km wide for a temporal window of the order of (at most) several weeks. This spatiotemporal domain is also the one in which the mesoscale activity induces through horizontal stirring a strong variability in the biogeochemical tracers, with ephemeral, local contrasts which can easily mask the regional and seasonal gradients. Therefore, whenever local in-situ measures are used to infer larger scale budgets one faces the challenge of identifying the mesoscale structuring effect, if not simply to filter it out. In the case of the KEOPS2 investigation of biogeochemical responses to natural iron fertilization, this problem was tackled by designing an adaptive sampling strategy based on regionally-optimized multisatellite products analyzed in real time by specifically designed Lagrangian diagnostics. This strategy identified the different mesoscale and stirring structures present in the region and tracked the dynamical frontiers among them. It also enabled back-trajectories for the ship sampled stations to be estimated, providing important insights into the timing and pathways of iron supply, which were explored further using model based on first order iron removal. This context was essential for the interpretation of the field results. The mesoscale circulation based strategy was also validated post-cruise by comparing the Lagrangian maps derived from satellite with the patterns of more than one hundred drifters adaptively released during KEOPS2 and a subsequent research voyage. The KEOPS2 strategy was adapted to the specific biogeochemical characteristics of the region, but its principles are general and will be useful for future in-situ biogeochemical surveys.

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