@article{8525,
  abstract     = {Let M be a smooth compact manifold of dimension at least 2 and Diffr(M) be the space of C r smooth diffeomorphisms of M. Associate to each diffeomorphism f;isin; Diffr(M) the sequence P n (f) of the number of isolated periodic points for f of period n. In this paper we exhibit an open set N in the space of diffeomorphisms Diffr(M) such for a Baire generic diffeomorphism f∈N the number of periodic points P n f grows with a period n faster than any following sequence of numbers {a n } n ∈ Z + along a subsequence, i.e. P n (f)>a ni for some n i →∞ with i→∞. In the cases of surface diffeomorphisms, i.e. dim M≡2, an open set N with a supergrowth of the number of periodic points is a Newhouse domain. A proof of the man result is based on the Gontchenko–Shilnikov–Turaev Theorem [GST]. A complete proof of that theorem is also presented.},
  author       = {Kaloshin, Vadim},
  issn         = {0010-3616},
  journal      = {Communications in Mathematical Physics},
  keywords     = {Mathematical Physics, Statistical and Nonlinear Physics},
  pages        = {253--271},
  publisher    = {Springer Nature},
  title        = {{Generic diffeomorphisms with superexponential growth of number of periodic orbits}},
  doi          = {10.1007/s002200050811},
  volume       = {211},
  year         = {2000},
}

@article{2729,
  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. As in [LSY-II] for homogeneous 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 in our companion paper [ES-I].},
  author       = {Erdös, László and Solovej, Jan},
  issn         = {0010-3616},
  journal      = {Communications in Mathematical Physics},
  number       = {3},
  pages        = {599 -- 656},
  publisher    = {Springer},
  title        = {{Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields, II. Leading order asymptotic estimates}},
  doi          = {10.1007/s002200050181},
  volume       = {188},
  year         = {1997},
}

@article{2724,
  abstract     = {We study the generalizations of the well-known Lieb-Thirring inequality for the magnetic Schrödinger operator with nonconstant magnetic field. Our main result is the naturally expected magnetic Lieb-Thirring estimate on the moments of the negative eigenvalues for a certain class of magnetic fields (including even some unbounded ones). We develop a localization technique in path space of the stochastic Feynman-Kac representation of the heat kernel which effectively estimates the oscillatory effect due to the magnetic phase factor.},
  author       = {Erdös, László},
  issn         = {0010-3616},
  journal      = {Communications in Mathematical Physics},
  number       = {3},
  pages        = {629 -- 668},
  publisher    = {Springer},
  title        = {{Magnetic Lieb-Thirring inequalities}},
  doi          = {10.1007/BF02099152},
  volume       = {170},
  year         = {1995},
}

@article{2722,
  abstract     = {A version of the one-dimensional Rayleigh gas is considered: a point particle of mass M (molecule), confined to the unit interval [0,1], is surrounded by an infinite ideal gas of point particles of mass 1 (atoms). The molecule interacts with the atoms and with the walls via elastic collision. Central limit theorems are proved for a wide class of additive functionals of this system (e.g. the number of collisions with the walls and the total length of the molecular path).},
  author       = {Erdös, László and Tuyen, Dao},
  issn         = {0010-3616},
  journal      = {Communications in Mathematical Physics},
  number       = {3},
  pages        = {451 -- 466},
  publisher    = {Springer},
  title        = {{Central limit theorems for the one-dimensional Rayleigh gas with semipermeable barriers}},
  doi          = {10.1007/BF02099260},
  volume       = {143},
  year         = {1992},
}