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 $2,3$ 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