| Abstract: |
| We prove the local existence of a gradient flow of the SRB entropy
functional on a Hilbert manifold of expanding maps on a circle with a Sobolev norm in its tangent space.
In a simple case, we obtain an explicit formula for the flow`s ordinary differential equation representation.
This gradient flow has a close connection to an interesting nonlinear partial differential equation:
a gradient-dependent diffusion equation, u_t u_x = u_{xx}. |
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