Invariance of stretching and expansion spectra, and Oseledec' multiplicative ergodic theorem

✍ Scribed by Yves Elskens

• Book ID: 104297085
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 203 KB
• Volume: 100
• Category: Article
• ISSN: 0167-2789
• DOI: 10.1016/s0167-2789(96)00184-4

✦ Synopsis

The local stretching rate a expresses the logarithmic divergence of trajectories along the local unstable manifold in phase space. We show that its distribution S(a) in an ergodic component is invariant with respect to the initial condition (almost surely) but depends on the coordinate system in which this dynamics is studied; the same applies to its moments. Only the average f aS(a) da, which is the largest Liapunov exponent, is invariant with respect to changes of coordinates. The same argument applies to higher-dimensional expansion spectra.