A Smooth Approximation on the Edge of Chaos
نویسنده
چکیده
It is known that for almost all starting points the non-deterministic dynamical system corresponding to a hyperbolic iterated function system with probabilities generates orbits whose frequency of visits to any given Borel subset of the domain is described by the unique invariant measure of the iterated function system with probabilities. In this paper, we will show that under certain conditions this chaotic probability measure can be approximated by a smooth probability density. We apply this result to forgetful neural networks.
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