CONSTRUCTING THE BOWEN MEASURE FOR AN ANOSOV DIFFEOMORPHISM
Ключевые слова:
Toral hyperbolic automorphism, stable and unstable currents, topological entropy, measure-theoretic entropy, Bowen measure, dynamical systems.Аннотация
This paper explores the construction of stable and unstable currents associated with toral hyperbolic automorphisms . A toral hyperbolic automorphism is defined by an invertible matrix with no eigenvalues on the unit circle, inducing a diffeomorphism on the torus . We describe the decomposition of the tangent bundle into stable and unstable subspaces and construct the corresponding stable and unstable currents by integrating over the stable and unstable manifolds. Additionally, we examine the entropy of these automorphisms, showing that the topological entropy is determined by the logarithm of the absolute values of the unstable eigenvalues of the matrix . An example of a 2-dimensional toral hyperbolic automorphism is provided to illustrate the entropy calculation. The relationship between entropy and the constructed currents is discussed, highlighting the role of the Bowen measure in maximizing entropy. This study contributes to the understanding of the dynamical properties and complexity of toral hyperbolic automorphisms.
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