Exemplos de descontinuidade para os expoentes de Lyapunov

Abstract

This work presents in an expanded form the construction of two examples of discontinuity of the Lyapunov exponents of a linear cocycle that takes values in SL(2,R) relative to topology α-Hölder, with α ∈ (0,∞). The hypothesis that the first example of discontinuity uses is the inequality 2^{2α} < σ, for some σ > 1, while the second example will use the hypothesis of σ^{2} > 2^{α}, so that p ∈ (1/2 ,1) is chosen close enough to 1 and σ^{4p−2} ≥ 2^{α} occurs. In particular, the second example of discontinuity covers the first example when the inequality σ^{2 }> 2^{4α} is used.