4 papers
Symplectic twist maps without conjugate points
M. L. Bialy, R. S. MacKay
We consider a sequences of symplectic twist maps corresponding to Frenkel Kontorova variational functional. For such a sequence without conjugate points we construct an invariant L…
Shock formation for forced Burgers equation and application
M. Bialy
We study the inviscid Burgers equation in the presence of spatially periodic potential force. We prove that for foliated initial value problem there are always solutions developing…
Variational properties of a nonlinear elliptic equation and rigidity
M. L. Bialy, R. S. MacKay
We consider in this paper elliptic equations which are perturbations of Laplace's equation by a compactly supported potential. We show that in dimension greater than three for a wi…
Rigidity for periodic magnetic fields
M. L. Bialy
We study the motion of a charge on a conformally flat Riemannian torus in the presence of magnetic field. We prove that for any non-zero magnetic field there always exist orbits of…