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A gentle introduction to anisotropic Banach spaces. (arXiv:1809.10785v1 [math.DS])
来源于:arXiv
The use of anisotropic Banach spaces has provided a wealth of new results in
the study of hyperbolic dynamical systems in recent years, yet their
application to specific systems is often technical and difficult to access. The
purpose of this note is to provide an introduction to the use of these spaces
in the study of hyperbolic maps and to highlight the important elements and how
they work together. This is done via a concrete example of a family of
dissipative Baker's transformations. Along the way, we prove an original result
connecting such transformations with expanding maps via a continuous family of
transfer operators acting on a single Banach space. 查看全文>>