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arXiv · 1606.02428

The linear request problem

Benoît Kloeckner
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Abstract

We propose a simple approach to a problem introduced by Galatolo and Pollicott, consisting in perturbing a dynamical system in order for its absolutely continuous invariant measure to change in a prescribed way. Instead of using transfer operators, we observe that restricting to an infinitesimal conjugacy already yields a solution. This allows us to work in any dimension and dispense from any dynamical hypothesis. In particular, we don't need to assume hyperbolicity to obtain a solution, although expansion moreover ensures the existence of an infinite-dimensional space of solutions.

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Benoît Kloeckner. 2016-06-08. The linear request problem. https://arxiv.org/abs/1606.02428

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