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Livsic Regularity For Markov Systems
Henk Bruin, Mark Holland, Matthew Nicol
We prove measurable Livsic theorems for dynamical systems modelled by Markov Towers. Our regularity results apply to solutions of cohomological equations posed on Henon-like mappin…
Topological invariance of the sign of the Lyapunov exponents in one-dimensional maps
Henk Bruin, Stefano Luzzatto
We explore some properties of Lyapunov exponents of measures preserved by smooth maps of the interval, and study the behaviour of the Lyapunov exponents under topological conjugacy…
A new proof of the Stable Manifold Theorem for hyperbolic fixed points on surfaces
Mark Holland, Stefano Luzzatto
We introduce a new technique for proving the classical Stable Manifold theorem for hyperbolic fixed points. This method is much more geometrical than the standard approaches which…
Normal Forms and Unfoldings of Linear Systems in Eigenspaces of (Anti)-Automorphisms of Order Two
I. Hoveijn, J. S. W. Lamb, R. M. Roberts
In this article we classify normal forms and unfoldings of linear maps in eigenspaces of (anti)-automorphisms of order two. Our main motivation is provided by applications to linea…