@article{179, abstract = {An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariski dense subset of the biprojective hypersurface x1y21+⋯+x4y24=0 in ℙ3×ℙ3. This confirms the modified Manin conjecture for this variety, in which the removal of a thin set of rational points is allowed.}, author = {Browning, Timothy D and Heath Brown, Roger}, issn = {0012-7094}, journal = {Duke Mathematical Journal}, number = {16}, pages = {3099--3165}, publisher = {Duke University Press}, title = {{Density of rational points on a quadric bundle in ℙ3×ℙ3}}, doi = {10.1215/00127094-2020-0031}, volume = {169}, year = {2020}, } @article{8423, abstract = {In this paper we show that for a generic strictly convex domain, one can recover the eigendata corresponding to Aubry–Mather periodic orbits of the induced billiard map from the (maximal) marked length spectrum of the domain.}, author = {Huang, Guan and Kaloshin, Vadim and Sorrentino, Alfonso}, issn = {0012-7094}, journal = {Duke Mathematical Journal}, number = {1}, pages = {175--209}, publisher = {Duke University Press}, title = {{On the marked length spectrum of generic strictly convex billiard tables}}, doi = {10.1215/00127094-2017-0038}, volume = {167}, year = {2017}, } @article{8505, abstract = {The classical principle of least action says that orbits of mechanical systems extremize action; an important subclass are those orbits that minimize action. In this paper we utilize this principle along with Aubry-Mather theory to construct (Birkhoff) regions of instability for a certain three-body problem, given by a Hamiltonian system of 2 degrees of freedom. We believe that these methods can be applied to construct instability regions for a variety of Hamiltonian systems with 2 degrees of freedom. The Hamiltonian model we consider describes dynamics of a Sun-Jupiter-comet system, and under some simplifying assumptions, we show the existence of instabilities for the orbit of the comet. In particular, we show that a comet which starts close to an orbit in the shape of an ellipse of eccentricity e=0.66 can increase in eccentricity up to e=0.96. In the sequels to this paper, we extend the result to beyond e=1 and show the existence of ejection orbits. Such orbits are initially well within the range of our solar system. This might give an indication of why most objects rotating around the Sun in our solar system have relatively low eccentricity.}, author = {Galante, Joseph and Kaloshin, Vadim}, issn = {0012-7094}, journal = {Duke Mathematical Journal}, keywords = {General Mathematics}, number = {2}, pages = {275--327}, publisher = {Duke University Press}, title = {{Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action}}, doi = {10.1215/00127094-1415878}, volume = {159}, year = {2011}, } @article{2730, abstract = {We give the leading order semiclassical asymptotics for the sum of the negative eigenvalues of the Pauli operator (in dimension two and three) with a strong non-homogeneous magnetic field. This result can be used to prove that the magnetic Thomas-Fermi theory gives the leading order ground state energy of large atoms. We develop a new localization scheme well suited to the anisotropic character of the strong magnetic field. We also use the basic Lieb-Thirring estimate obtained earlier (1996). (orig.) 19 refs.}, author = {Erdös, László and Solovej, Jan}, issn = {0012-7094}, journal = {Duke Mathematical Journal}, number = {1}, pages = {127 -- 173}, publisher = {Duke University Press}, title = {{Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate}}, doi = {10.1215/S0012-7094-99-09604-7}, volume = {96}, year = {1999}, } @article{2713, author = {Erdös, László}, issn = {0012-7094}, journal = {Duke Mathematical Journal}, number = {2}, pages = {541 -- 566}, publisher = {Duke University Press}, title = {{Estimates on stochastic oscillatory integrals and on the heat kernel of the magnetic Schrödinger operator}}, doi = {10.1215/S0012-7094-94-07619-9}, volume = {76}, year = {1994}, }