Chaotic Properties of Subshifts Generated by a Non-Periodic Recurrent Orbit

The chaotic properties of some subshift maps are investigated. These subshifts are the orbit closures of certain non-periodic recurrent points of a shift map. We first provide a review of basic concepts for dynamics of continuous maps in metric spaces. These concepts include nonwandering point, recurrent point, eventually periodic point, scrambled set, sensitive dependence on initial conditions, Robinson chaos, and topological entropy. Next we review the notion of shift maps and subshifts. Then we show that the one-sided subshifts generated by a non-periodic recurrent point are chaotic in the sense of Robinson. Moreover, we show that such a subshift has an infinite scrambled set if it has a periodic point. Finally, we give some examples and discuss the topological entropy of these subshifts, and present two open problems on the dynamics of subshifts

Is the f0(600)f_0(600) meson a dynamically generated resonance? -- a lesson learned from the O(N) model and beyond

O(N) linear $\sigma$ model is solvable in the large $N$ limit and hence provides a useful theoretical laboratory to test various unitarization approximations. We find that the large $N_c$ limit and the $m_\sigma\to \infty$ limit do not commute. In order to get the correct large $N_c$ spectrum one has to firstly take the large $N_c$ limit. We argue that the $f_0(600)$ meson may not be described as generated dynamically. On the contrary, it is most appropriately described at the same level as the pions, i.e, both appear explicitly in the effective lagrangian. Actually it is very likely the $\sigma$ meson responsible for the spontaneous chiral symmetry breaking in a lagrangian with linearly realized chiral symmetry.Comment: 15 pages, 3 figurs; references added; discussions slightly modified; revised version accepted by IJMP