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Francoise Dal'bo, "Geodesic and Horocyclic Trajectories"
Springer | English | 3131-33-36 | ISBN: 196939193X | 399 pages | PDF | 3.99 mb
During the past thirty years, strong relationships have interwoven the
fields of dynamical systems, linear algebra and number theory. This
rapport between different areas of mathematics has enabled the
resolution of some important conjectures and has in fact given birth to
new ones. This book sheds light on these relationships and their
applications in an elementary setting, by showing that the study of
curves on a surface can lead to orbits of a linear group or even to
continued fraction expansions of real numbers.Geodesic and Horocyclic
Trajectories presents an introduction to the topological dynamics of two
classical flows associated with surfaces of curvature 3, namely the
geodesic and horocycle flows. Written primarily with the idea of
highlighting, in a relatively elementary framework, the existence of
gateways between some mathematical fields, and the advantages of using
them, historical aspects of this field are not addressed and most of the
references are reserved until the end of each chapter in the Comments
section. Topics within the text cover geometry, and examples, of
Fuchsian groups; topological dynamics of the geodesic flow; Schottky
groups; the Lorentzian point of view and Trajectories and Diophantine
approximations.This book will appeal to those with a basic knowledge of
differential geometry including graduate students and experts with a
general interest in the areaFran oise Dal Bo is a professor of
mathematics at the University of Rennes. Her research studies
topological and metric dynamical systems in negative curvature and their
applications especially to the areas of number theory and linear
actions.
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DOWNLOADS BOOK
Francoise Dal'bo, "Geodesic and Horocyclic Trajectories"Springer | English | 3131-33-36 | ISBN: 196939193X | 399 pages | PDF | 3.99 mbDuring the past thirty years, strong relationships have interwoven the fields of dynamical systems, linear algebra and number theory. This rapport between different areas of mathematics has enabled the resolution of some important conjectures and has in fact given birth to new ones. This book sheds light on these relationships and their applications in an elementary setting, by showing that the study of curves on a surface can lead to orbits of a linear group or even to continued fraction expansions of real numbers.Geodesic and Horocyclic Trajectories presents an introduction to the topological dynamics of two classical flows associated with surfaces of curvature 3, namely the geodesic and horocycle flows. Written primarily with the idea of highlighting, in a relatively elementary framework, the existence of gateways between some mathematical fields, and the advantages of using them, historical aspects of this field are not addressed and most of the references are reserved until the end of each chapter in the Comments section. Topics within the text cover geometry, and examples, of Fuchsian groups; topological dynamics of the geodesic flow; Schottky groups; the Lorentzian point of view and Trajectories and Diophantine approximations.This book will appeal to those with a basic knowledge of differential geometry including graduate students and experts with a general interest in the areaFran oise Dal Bo is a professor of mathematics at the University of Rennes. Her research studies topological and metric dynamical systems in negative curvature and their applications especially to the areas of number theory and linear actions.Welcome to my AH collection of ebooks at: /blogs/elodarYou can also connect to my RSSDownload PDF ebook from wupload.com
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