000 03427nam a22004935i 4500
001 978-0-85729-073-1
003 DE-He213
005 20140220083712.0
007 cr nn 008mamaa
008 101112s2011 xxk| s |||| 0|eng d
020 _a9780857290731
_9978-0-85729-073-1
024 7 _a10.1007/978-0-85729-073-1
_2doi
050 4 _aQA313
072 7 _aPBWR
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515.39
_223
082 0 4 _a515.48
_223
100 1 _aDal’Bo, Françoise.
_eauthor.
245 1 0 _aGeodesic and Horocyclic Trajectories
_h[electronic resource] /
_cby Françoise Dal’Bo.
264 1 _aLondon :
_bSpringer London,
_c2011.
300 _aXII, 176p. 110 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUniversitext
505 0 _aDynamics of Fuchsian groups -- Examples of Fuchsian Groups -- Topological dynamics of the geodesic flow -- Schottky groups -- Topological dynamics -- The Lorentzian point of view -- Trajectories and Diophantine approximations.
520 _aDuring 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 −1, 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 area Françoise 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.
650 0 _aMathematics.
650 0 _aDifferentiable dynamical systems.
650 0 _aGlobal differential geometry.
650 0 _aNumber theory.
650 1 4 _aMathematics.
650 2 4 _aDynamical Systems and Ergodic Theory.
650 2 4 _aNumber Theory.
650 2 4 _aDifferential Geometry.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780857290724
830 0 _aUniversitext
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-85729-073-1
912 _aZDB-2-SMA
999 _c105122
_d105122