动力学不稳定性的几何描述--使用非仿射参数化--与传统的切线动力学之间的普遍分歧
General disagreement between the Geometrical Description of Dynamical In-stability -using non affine parameterizations- and traditional Tangent Dynamics
摘要：
本文讨论了几何李雅普诺夫指数与切向动力学中的李雅普诺夫指数的一般不一致。它是在一个相当普遍的方式表明，矢量场的测地线扩展$ξ^k_G$是不等价的切线动力学矢量$ξ^k_T$，如果参数化是不仿射的，并在几何框架中获得的动力学稳定性的结果可以定性地不同于那些在切线动力学。它也证明了在Jacobi度量的情况下，通常使用的非仿射参数化，$ξ^k_G$满足微分方程，不同于切线动力学方程的参数共振，因此，正指数的系统在稳定的制度。
英文摘要：
In this paper, the general disagreement of the geometrical lyapunov exponent with lyapunov exponent from tangent dynamics is addressed. It is shown in a quite general way that the vector field of geodesic spread $ξ^k_G$ is not equivalent to the tangent dynamics vector $ξ^k_T$ if the parameterization is not affine and that results regarding dynamical stability obtained in the geometrical framework can differ qualitatively from those in the tangent dynamics. It is also proved in a general way that in the case of Jacobi metric -frequently used non affine parameterization-, $ξ^k_G$ satisfies differential equations which differ from the equations of the tangent dynamics in terms that produce parametric resonance, therefore, positive exponents for systems in stable regimes.
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