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- W2009754703 abstract "Using a simple 2D area-preserving map we study the evolution of the deviation vector ξ of two initially nearby orbits. It is known that the deviation vector in each point is aligned along a preferable direction, which in the case of regular orbits is the direction of the tangent line to the invariant curve at that point, having also a specific value defined as the `stretching number' at this point. Before the deviation vector takes its preferred direction and value it passes through a transient period. This transient period is found to be very short in the case of chaotic orbits while it is quite long for regular orbits. The initial orientation plays a minor role on the length of the transition phase except in the case when the initial ξ is almost perpendicular to the invariant curve. In this latter case the transition phase becomes quite extended. Analytic calculations suggest that as the iteration number n increases, in the case of chaotic orbits, the deviation vector tends to its preferred value exponentially, while it evolves with an n-1 power law in the case of regular orbits. Numerical results support the analytic predictions." @default.
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- W2009754703 date "2001-02-09" @default.
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- W2009754703 title "The transition phase of the deviation vector of nearby orbits" @default.
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- W2009754703 doi "https://doi.org/10.1088/0305-4470/34/7/322" @default.
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