Integer lattices of the action variables for the generalized Lagrange case

Kantonistova, E. O.

doi:10.3103/s0027132212010068

Search citation statements

Order By: Relevance

Paper Sections

Select...

And Besides the Bifurcation Diagram May Consist Of Only One1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2013

2016

Publication Types

Select...

Article3

Book2

Relationship

Self Cite1

Independent4

Authors

Journals

Cited by 5 publications

(1 citation statement)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Example 2.1 Let us consider a function f (r) = sin r (this system called a "spherical pendulum system" (this system was studied in [13])). In this case, the bifurcation diagram has a very simple form: it has no curves of type (iii).…”

Section: And Besides the Bifurcation Diagram May Consist Of Only Onementioning

confidence: 99%

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

Фоменко

Kantonistova

2015

Studies in Systems, Decision and Control

Self Cite

View full text Add to dashboard Cite

show abstract

Section: And Besides the Bifurcation Diagram May Consist Of Only Onementioning

confidence: 99%

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

Фоменко

Kantonistova

2015

Studies in Systems, Decision and Control

Self Cite

View full text Add to dashboard Cite

show abstract

Algebra and Geometry Through Hamiltonian Systems

Фоменко

Konyaev

2013

Continuous and Distributed Systems

View full text Add to dashboard Cite

Closed geodesics on piecewise smooth surfaces of revolution with constant curvature

Sypchenko¹,

Timonina²

2015

Sb. Math.

View full text Add to dashboard Cite

We present a model for laser cooling of a single ion in the Penning trap. The model solves the equations of motion in the presence of the damping caused by the interaction with the laser beam, and predicts for the first time the dependence of the cooling rates for the two radial degrees of freedom in the trap as a function of the laser detuning, laser beam offset and saturation parameter. The conditions derived for both radial degrees of freedom to be cooled simultaneously agree with those found in earlier studies. The results indicate that under conditions where both motions are cooled simultaneously, the cooling rates are both significantly smaller than the maximum rate for either motion considered in isolation. Furthermore, the magnetron cooling rate is typically much lower than the cyclotron cooling rate, as has been found in experiments. The model indicates how the cooling rate for a single ion may be optimized. †

show abstract

Integer lattices of the action variables for the generalized Lagrange case

Cited by 5 publications

References 3 publications

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

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

Algebra and Geometry Through Hamiltonian Systems

Closed geodesics on piecewise smooth surfaces of revolution with constant curvature

Contact Info

Product

Resources

About