Margulis Measures on Expanding Foliations: Construction and Rigidity

What the math gives to ML

The paper constructs reference measures on one-dimensional expanding leaves whose pushforward scales by a constant entropy factor. It also shows that maximal leaf-entropy measures have conditional measures equivalent to these references, and that a leafwise log-Jacobian can be cohomologous to a constant. A transferable neural mechanism is to regularize a recurrent transition so that expansion along a learned state direction is nearly constant across states. This gives a measurable dynamical signature through the variance of corrected log expansion and the estimated finite-time Lyapunov exponent.