6,715 research outputs found
On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties
Let f : X --> X be a dominant rational map of a projective variety defined
over a global field, let d_f be the dynamical degree of f, and let h_X be a
Weil height on X relative to an ample divisor. We prove that h_X(f^n(P)) <<
(d_f + e)^n h_X(P), where the implied constant depends only on X, h_X, f, and
e. As applications, we prove a fundamental inequality a_f(P) \le d_f for the
upper arithmetic degree and we construct canonical heights for (nef) divisors.
We conjecture that a_f(P) = d_f whenever the orbit of P is Zariski dense, and
we describe some cases for which we can prove our conjecture.Comment: 32 page
Friction, order, and transverse pinning of a two-dimensional elastic lattice under periodic and impurity potentials
Frictional phenomena of two-dimensional elastic lattices are studied
numerically based on a two-dimensional Frenkel-Kontorova model with impurities.
It is shown that impurities can assist the depinning. We also investigate
anisotropic ordering and transverse pinning effects of sliding lattices, which
are characteristic of the moving Bragg glass state and/or transverse glass
state. Peculiar velocity dependence of the transverse pinning is observed in
the presence of both periodic and random potentials and discussed in the
relation with growing order and discommensurate structures.Comment: RevTeX, 4 pages, 5 figures. to appear in Phys. Rev. B Rapid Commu
- …