Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, specifically in topology, a pseudo-Anosov map is a type of a diffeomorphism or homeomorphism of a surface. It is a generalization of a linear Anosov diffeomorphism of the torus. Its definition relies on the notion of a measured foliation invented by William Thurston, who also coined the term "pseudo-Anosov diffeomorphism" when he proved his...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, specifically in topology, a pseudo-Anosov map is a type of a diffeomorphism or homeomorphism of a surface. It is a generalization of a linear Anosov diffeomorphism of the torus. Its definition relies on the notion of a measured foliation invented by William Thurston, who also coined the term "pseudo-Anosov diffeomorphism" when he proved his classification of diffeomorphisms of a surface. A measured foliation F on a closed surface S is a geometric structure on S which consists of a singular foliation and a measure in the transverse direction. In some neighborhood of a regular point of F, there is a "flow box" : U -> R2 which sends the leaves of F to the horizontal lines in R2. The notion of a diffeomorphism of S is redefined with respect to this modified differentiable structure. With some technical modifications, these definitions extend to the case of a surface with boundary.
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