We study the spin fluctuation dynamics of Cu-O chains in the oxygen deficient planes of YBa2Cu3O6+x. The chains are described by a model including antiferromagnetic interactions between the spins and Kondo-like scattering of the oxygen holes by the copper spins. There are incommensurate spin fluctuations along the direction of the chains. The dynamic structure factor of this system is qualitatively different from that of a quasi one-dimensional localized antiferromagnet due to the presence of itinerant holes. We compute the dynamic structure factor that could be measured in neutron scattering experiments. Key words: Quantized spin models; Dynamic properties; Y-based cuprates; Neutron scattering techniques The oxygen deficient CuOx planes play an important role in the physics of the high-Tc compounds YBa2Cu3O6+x. These planes are composed of Cun+1On chain fragments in which Cu and O atoms form a linear alternating chain. The physical properties of the chain planes are dominated by the longest chain fragments. To a first approximation, these chains may be viewed as decoupled from each other and from the CuO2 planes. Therefore, important one-dimensional fluctuation effects are expected in the charge and spin excitation spectra of the CuOx planes. The low-energyspin dynamics of this system was studied theoretically in  within a strong-coupling model in which every Cu site is occupied by a hol
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