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Concept

Action-angle coordinates

Publications associées (9)

Stability of a Point Charge for the Vlasov–Poisson System: The Radial Case

Klaus Martin Widmayer

We consider the Vlasov–Poisson system with repulsive interactions. For initial data a small, radial, absolutely continuous perturbation of a point charge, we show that the solution is global and disperses to infinity via a modified scattering along traject ...

2021

Mechanical and hydraulic transport properties of transverse-isotropic Gneiss deformed under deep reservoir stress and pressure conditions

Marie Estelle Solange Violay, Mateo Alejandro Acosta

In central Europe, many geo-energy reservoirs have revealed to be hosted in transverse isotropic crystalline rock, where the rock's mechanical and hydraulic transport properties are poorly constrained. Here, we performed triaxial experiments on Cresciano G ...

2020

The Geometric Nature of the Flaschka Transformation

Tudor Ratiu, François Gay-Balmaz

We show that the Flaschka map, originally introduced to analyze the dynamics of the integrable Toda lattice system, is the inverse of a momentum map. We discuss the geometrical setting of the map and apply it to the generalized Toda lattice systems on semi ...

Springer Verlag2017

Revisiting the quest for a universal log-law and the role of pressure gradient in "canonical" wall-bounded turbulent flows

Peter Monkewitz

The trinity of so-called "canonical" wall-bounded turbulent flows, comprising the zero pressure gradient turbulent boundary layer, abbreviated ZPG TBL, turbulent pipe flow, and channel/duct flows has continued to receive intense attention as new and more r ...

Amer Physical Soc2017

Asymptotics of action variables near semi-toric singularities

The presence of focus-focus singularities in semi-toric integrables Hamiltonian systems is one of the reasons why there cannot exist global Action-Angle coordinates on such systems. At focus-focus critical points, the Liouville-Arnold-Mineur theorem does n ...

Elsevier2015

New Techniques For Obtaining Schubert-Type Formulas For Hamiltonian Manifolds

Silvia Sabatini

In [GT], Goldin and Tolman extend some ideas from Schubert calculus to the more general setting of Hamiltonian torus actions on compact symplectic manifolds with isolated fixed points. (See also [Kn99,Kn08].) The main goal of this paper is to build on this ...

Int Press Boston, Inc2013

Static Models of Derivative-Coordinates Phase Spaces for Multivariate Time Series Classification: An Application to Signature Verification

Jonas Richiardi, Andrzej Drygajlo

Multivariate time series are sequences, whose order is provided by a time index; thus, most classifiers used on such data treat time as a special quantity, and encode it, structurally in a model. A typical example of such models is the hidden Markov model, ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2009

The Momentum Map In Poisson Geometry

Tudor Ratiu, Juan-Pablo Ortega

Every action on a Poisson manifold by Poisson diffeomorphisms lifts to a Hamiltonian action on its symplectic groupoid which has a canonically defined momentum map. We study various properties of this momentum map as well as its use in reduction. ...

2009

Quantum chaos? Genericity and nongenericity in the MHD spectrum of nonaxisymmetric toroidal plasmas

Ben McMillan

The eigenmode spectrum is a fundamental starting point for the analysis of plasma stability and the onset of turbulence, but the characterization of the spectrum even for the simplest plasma model, ideal magnetohydrodynamics (MHD), is not fully understood. ...

2007