Abstract
In this paper, we present a new method for obtaining lower bounds of the strict invariance entropy by combining an approach from the theory of escape rates and geometric methods used in the dimension theory of dynamical systems. For uniformly expanding systems and for inhomogeneous bilinear systems we can describe the lower bounds in terms of uniform volume growth rates on subbundles of the tangent bundle. In particular, we obtain criteria for positive entropy. We also apply the estimates to bilinear systems on projective space.
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