What question did this study set out to answer?

This research aims to identify a scenario where all but one ergodic invariant probability measure exhibit small Lyapunov exponents.

January 17, 2026

An isolated Lyapunov exponent

Puntos clave

This research aims to identify a scenario where all but one ergodic invariant probability measure exhibit small Lyapunov exponents.
Constructed a continuous linear cocycle
Explored expanding base dynamics
Analyzed ergodic invariant probability measures
Most ergodic measures have small Lyapunov exponents
One measure has significant Lyapunov exponents away from zero
The distinguished measure's support is not periodic, violating periodic approximation.

Resumen

We construct a continuous linear cocycle over an expanding base dynamics for which the Lyapunov exponents of all ergodic invariant probability measures are small, except for one measure whose Lyapunov exponents are away from zero. The support of this distinguished measure is not a periodic orbit and therefore our example violates the periodic approximation property.

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Cite This Study

Jairo Bochi (Thu,) studied this question.

synapsesocial.com/papers/696b2616d2a12237a93495cf https://doi.org/https://doi.org/10.1090/proc/17510