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Recently Guenther et al the globally diagonalized ${\alpha}^{2}$ dynamooperator spectrum [J Phys A 2007) in mean field media, and its Krein spacerelated perturbation theory [J Phys A 2006). Earlier, an example of fastdynamos in stretch shear and fold Anosov maps have been given by Gilbert [PRSA[1993)). In this paper, analytical solutions representing general turbulentdynamo filaments are obtained in resistive plasmas. When turbulent diffusivityis present and kinetic helicity vanishes, a fast dynamo mode is obtained, andthe Anosov eigenvalue obtained. The magnetic field lays down on a Frenet 2plane along the filaments embedded in a 3D flow. Curvature effects on fastdynamo are also investigate. In case of weak curvature filaments the onedimensional manifolds in plasmas present a fast dynamo action. A parallelresult has been obtained by Chicone et al [Comm Math Phys), in the case fastdynamo spectrum in two dimensional compact Riemannian manifolds of negativeconstant curvature, called Anosov spaces. While problems of embedding mayappear in their case here no embedding problems appear since the onedimensional curved plasmas are embedded in three dimensional Euclidean spaces.In the examples considered here, equipartion between normal and binormalcomponents of the magnetic field components is considered. In the oppositecase, non Anosov oscillatory, purely imaginary, branches of the spectrum arefound in dynamo manifold. Negative constant curvature non-compact$\textbf{H}^{2}$ manifold, has also been used in one-component electron 2Dplasma by Fantoni and Tellez (Stat. Phys, (2008))

Anosov branches of dynamo spectra in one dimensional plasmas