The top Lyapunov exponent of a primitive Markov quasi-periodic cocycle with simple top spectrum has a holomorphic extension in a complex neighborhood of the transition matrix.
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Analyticity of Lyapunov Exponents for Mixed Markov Quasi-Periodic Cocycles
The top Lyapunov exponent of a primitive Markov quasi-periodic cocycle with simple top spectrum has a holomorphic extension in a complex neighborhood of the transition matrix.