101,503 research outputs found
Labyrinthine pathways towards supercycle attractors in unimodal maps
We uncover previously unknown properties of the family of periodic
superstable cycles in unimodal maps characterized each by a Lyapunov exponent
that diverges to minus infinity. Amongst the main novel properties are the
following: i) The basins of attraction for the phases of the cycles develop
fractal boundaries of increasing complexity as the period-doubling structure
advances towards the transition to chaos. ii) The fractal boundaries, formed by
the preimages of the repellor, display hierarchical structures organized
according to exponential clusterings that manifest in the dynamics as
sensitivity to the final state and transient chaos. iii) There is a functional
composition renormalization group (RG) fixed-point map associated to the family
of supercycles. iv) This map is given in closed form by the same kind of
-exponential function found for both the pitchfork and tangent bifurcation
attractors. v) There is a final stage ultra-fast dynamics towards the attractor
with a sensitivity to initial conditions that decreases as an exponential of an
exponential of time.Comment: 8 pages, 13 figure
Meson decay in the Fock-Tani Formalism
The Fock-Tani formalism is a first principle method to obtain effective
interactions from microscopic Hamiltonians. Usually this formalism was applied
to scattering, here we introduced it to calculate partial decay widths for
mesons.Comment: Presented at HADRON05 XI. "International Conference on Hadron
Spectroscopy" Rio de Janeiro, Brazil, August 21 to 26, 200
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