Let $A(x,n)$ be the cocycle over $f$, where $f$ is a measure-preserving transformation on a probability space $X$. Is the largest Lyapunov exponent always given by:

$\lim_{n\to +\infty} \log ||A(x,n)||$?

Since the above limit can be bounded from above by $\int_X\log ||A||$, can one give an example of the cocycle where the above inequality is strict? Tnx!

Let $A(x,n)$ be the cocycle over $f$, where $f$ is a measure-preserving transformation on a probability space $X$. Is the largest Lyapunov exponent always given by:

$\lim_{n\to +\infty} \log \|A(x,n)\|$?

Since the above limit can be bounded from above by $\int_X\log \|A\|$, can one give an example of the cocycle where the above inequality is strict? Tnx!

Let A(x,n) be the cocycle over f, where f is an measure preserving transformation on a probability space X. Is the largest Lyapunov exponent always given by

\lim_{n\to +\infty} \log ||A(x,n)||?

Since the above limit can be bounded from above by \int_X\log ||A|| can one give an example of the cocycle where the above inequality is strict? Tnx!

Let $A(x,n)$ be the cocycle over $f$, where $f$ is a measure-preserving transformation on a probability space $X$. Is the largest Lyapunov exponent always given by:

$\lim_{n\to +\infty} \log ||A(x,n)||$?

Since the above limit can be bounded from above by $\int_X\log ||A||$, can one give an example of the cocycle where the above inequality is strict? Tnx!