In this article we explore to what extend the techniques of Piunikhin, Salamon and Schwarz in [PSS96] can be carried over to Lagrangian Floer homology. In [PSS96] the authors establish an isomorphism between Hamiltonian Floer homology and singular homology of the underlying symplectic manifold. In general, Lagrangian Floer homology is not isomorphic to the singular homology of the Lagrangian su...

This paper deals with the Lagrangian analogue of symplectic or point reduction by stages. We develop Routh reduction as a reduction technique that preserves the Lagrangian nature of the dynamics. To do so we heavily rely on the relation between Routh reduction and cotangent symplectic reduction. The main results in this paper are: (i) we develop a class of so called magnetic Lagrangian systems ...

To better understand the capacity of Lagrangian Stochastic Models to simulate superdiffusive and subdiffusive tracer motion in oceanic turbulence, we examine their performance on a simple class of model velocity fields which support subdiffusive or superdiffusive regimes of tracer transport associated to power-law regions of the Lagrangian power spectrum. We focus on how well the Lagrangian Sto...

In this paper we construct new examples of minimal Lagrangian submanifolds in the complex hyperbolic space with large symmetry groups, obtaining three 1-parameter families with cohomogeneity one. We characterize them as the only minimal Lagrangian submanifolds in CHn foliated by umbilical hypersurfaces of Lagrangian subspaces RHn of CHn. Several suitable generalizations of the above constructio...

My project addresses statistical and stochastic problems in the following fields: Lagrangian prediction (1), Lagrangian data assimilation (2), development and validation of Lagrangian stochastic models (LSM) (3). The long range scientific objectives of this study comprise rigorous determining limits of predictability for Lagrangian motion in semi-enclosed seas, littoral zones, and straits on ti...

Experimentalists now measure intense rotations of Lagrangian particles in turbulent flows by tracking their trajectories and Lagrangian-average velocity gradients at high Reynolds numbers. This paper formulates the dynamics of an orthonormal frame attached to each Lagrangian fluid particle undergoing three-axis rotations, by using quaternions in combination with Ertel’s theorem for frozen-in vo...

The main theorem of this paper asserts that the inclusion of the space of projective Lagrangian planes into the space of Lagrangian submanifolds of complex projective space induces an injective homomorphism of fundamental groups. We introduce three invariants of exact loops of Lagrangian submanifolds that are modelled on invariants introduced by Polterovich for loops of Hamiltonian symplectomor...