275 research outputs found
An extension of the Artin-Mazur theorem
Let M be a compact manifold. We call a mapping f in C^r(M,M) an Artin-Mazur
mapping if the number of isolated periodic points of f^n grows at most
exponentially in n. Artin and Mazur posed the following problem: What can be
said about the set of Artin-Mazur mappings with only transversal periodic
orbits? Recall that a periodic orbit of period n is called transversal if the
linearization df^n at this point has for an eigenvalue no nth roots of unity.
Notice that a hyperbolic periodic point is always transversal, but not vice
versa.
We consider not the whole space C^r(M,M) of mappings of M into itself, but
only its open subset Diff^r(M). The main result of this paper is the following
theorem: Let 1 <= r < \infty. Then the set of Artin-Mazur diffeomorphisms with
only hyperbolic periodic orbits is dense in the space Diff^r(M).Comment: 13 pages, published version, abstract added in migratio
Coexistence of periodic-2 and periodic-3 caustics for nearly circular analytic billiard maps
For symmetrically analytic deformation of the circle (with certain Fourier
decaying rate), the necessary condition for the corresponding billiard map to
keep the coexistence of periodic caustics is that the deformation has to
be an isometric transformation
Radiative decay of the dynamically generated open and hidden charm scalar meson resonances D_{s0}^*(2317) and X(3700)
We present the formalism for the decay of dynamically generated scalar mesons
with open- or hidden-charm and give results for the decay of D^*_{s0} (2317) to
\gamma D_s^* plus that of a hidden charm scalar meson state predicted by the
theory around 3700 MeV decaying into \gamma J/\psi.Comment: Appendix adde
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