We study the positivity of the Lyapunov exponent for a smooth SL(2, ℝ)-valued cocycle defined over a flow from a class which includes the Kronecker flows and others as well. We also discuss the question of the density in the Hölder class of the set of SL(2, ℝ)-cocycles exhibiting an exponential dichotomy when the base flow is of Kronecker type on a 2-torus.
On the Lyapunov Exponent of Certain SL(2, R)-Valued Cocycles II / R. FABBRI; R.JOHNSON; L.ZAMPOGNI. - In: DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS. - ISSN 0971-3514. - STAMPA. - 18:(2010), pp. 135-161. [10.1007/s12591-010-0003-0]
On the Lyapunov Exponent of Certain SL(2, R)-Valued Cocycles II
FABBRI, ROBERTA;JOHNSON, RUSSELL ALLAN;ZAMPOGNI, LUCA
2010
Abstract
We study the positivity of the Lyapunov exponent for a smooth SL(2, ℝ)-valued cocycle defined over a flow from a class which includes the Kronecker flows and others as well. We also discuss the question of the density in the Hölder class of the set of SL(2, ℝ)-cocycles exhibiting an exponential dichotomy when the base flow is of Kronecker type on a 2-torus.
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