03139nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185245020300207260008200410300003400492336002600526337002600552338003600578347002400614490006100638505029800699506006600997520138001063650003502443650004602478650003102524700003502555700003602590700003002626856003202656856006502688211-161121CH-001817-320161121234501.0a fot ||| 0|cr nn mmmmamaa161121e20161130sz fot ||| 0|eng d a978303719668770a10.4171/1682doi ach0018173 7aPBKJ2bicssc a37-xxa53-xx2msc10aDynamics Done with Your Bare Handsh[electronic resource] :bLecture notes by Diana Davis, Bryce Weaver, Roland K. W. Roeder, Pablo Lessa /cFrançoise Dal’Bo, François Ledrappier, Amie Wilkinson3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2016 a1 online resource (214 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-517600tLines in positive genus: An introduction to flat surfaces /rDiana Davis --tIntroduction to complicated behavior and periodic orbits /rBryce Weaver --tAround the boundary of complex dynamics /rRoland K.W. Roeder --tRecurrence vs transience: An introduction to random walks /rPablo Lessa.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book arose from 4 lectures given at the Undergraduate Summer School of the Thematic Program Dynamics and Boundaries held at the University of Notre Dame. It is intended to introduce (under)graduate students to the field of dynamical systems by emphasizing elementary examples, exercises and bare hands constructions.
The lecture of Diana Davis is devoted to billiard flows on polygons, a simple-sounding class of continuous time dynamical system for which many problems remain open.
Bryce Weaver focuses on the dynamics of a 2x2 matrix acting on the flat torus. This example introduced by Vladimir Arnold illustrates the wide class of uniformly hyperbolic dynamical systems, including the geodesic flow for negatively curved, compact manifolds.
Roland Roeder considers a dynamical system on the complex plane governed by a quadratic map with a complex parameter. These maps exhibit complicated dynamics related to the Mandelbrot set defined as the set of parameters for which the orbit remains bounded.
Pablo Lessa deals with a type of non-deterministic dynamical system: a simple walk on an infinite graph, obtained by starting at a vertex and choosing a random neighbor at each step. The central question concerns the recurrence property. When the graph is a Cayley graph of a group, the behavior of the walk is deeply related to algebraic properties of the group.07aDifferential equations2bicssc07aDynamical systems and ergodic theory2msc07aDifferential geometry2msc1 aDal’Bo, Françoise,eeditor.1 aLedrappier, François,eeditor.1 aWilkinson, Amie,eeditor.40uhttps://doi.org/10.4171/168423cover imageuhttps://www.ems-ph.org/img/books/dalbo_mini.jpg