Zobrazeno 1 - 10
of 581
pro vyhledávání: '"Mackay, Robert"'
For an untilted Frenkel-Kontorova chain and any rational $p/q$, Aubry and Mather proved there are minimising equilibrium states that are left- and right-asymptotic to neighbouring pairs of spatially periodic minimisers of type $(p,q)$. They are known
Externí odkaz:
http://arxiv.org/abs/2408.14124
Autor:
MacKay, Robert S.
The paper describes ways that the computation of the volume enclosed by an invariant torus (flux surface) for a magnetic field can be reduced from a 3D integral to a 2D integral.
Externí odkaz:
http://arxiv.org/abs/2406.12372
A Converse KAM method for 3D vector fields, establishing regions through which pass no invariant 2-tori transverse to a given direction field, is tested on some helical perturbations of an axisymmetric magnetic field in toroidal geometry. It finds re
Externí odkaz:
http://arxiv.org/abs/2304.09613
We present an example of a monotone two-parameter family of vector fields on a torus whose bifurcation diagram we demonstrate to be in the class of "simplest" diagrams proposed by Baesens & MacKay (2018 Nonlinearity 31 2928--81). This shows that the
Externí odkaz:
http://arxiv.org/abs/2207.04031
Autor:
MacKay, Robert S
For Schrodinger operators with suitable 1D potentials, focussing particularly on those that go to infinity at infinity, a characteristic function is constructed, via shooting functions. It is proved to be entire and its zeroes to be the eigenvalues.
Externí odkaz:
http://arxiv.org/abs/2205.04070
Autor:
MacKay, Robert S
In this paper it is proved that for families of stochastic operators on a countable tensor product, depending smoothly on parameters, any spectral projection persists smoothly, where smoothness is defined using norms based on ideas of Dobrushin. A ri
Externí odkaz:
http://arxiv.org/abs/2204.06419
A method to establish regions of phase space through which pass no invariant tori transverse to a given direction field is applied to the planar circular restricted three-body problem. Implications for the location of stable orbits for planets around
Externí odkaz:
http://arxiv.org/abs/2202.12691