On Geometry, Arithmetics and Chaos

Abstract: Our main result is that chaos in dimension $n+1$ is a one-dimensional geometrical object embedded in a geometrical object of dimension $n$ which corresponds to a $n$ dimensional object which is either singular or non-singular. Our main result is then that this chaos occurs in the first case as either on an isolated or non-isolated singularity. In the first case this chaos is either boundary chaos or spherical chaos which is what happens also in the non-singular case. In the case of an isolated singular geometry one has chaos which can either be boundary, spherical or tubular chaos. We furthermore prove that the prime numbers display quantum behaviour.