Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of Oseledets’ splitting
2012 ◽
Vol 33
(3)
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pp. 693-712
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Keyword(s):
The Mean
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AbstractWe consider locally minimizing measures for conservative twist maps of the $d$-dimensional annulus and for Tonelli Hamiltonian flows defined on a cotangent bundle $T^*M$. For weakly hyperbolic measures of such type (i.e. measures with no zero Lyapunov exponents), we prove that the mean distance/angle between the stable and unstable Oseledets bundles gives an upper bound on the sum of the positive Lyapunov exponents and a lower bound on the smallest positive Lyapunov exponent. We also prove some more precise results.
2000 ◽
Vol 32
(01)
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pp. 244-255
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Keyword(s):
Keyword(s):
2013 ◽
Vol 438
(11)
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pp. 4448-4468
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