03412nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020001800100020001900118024003500137040000900172082001500181082001500196100002900211245014100240264004600381300002100427336002600448337002600474338003900500347002400539490005200563505040300615520139601018650001702414650003502431650003802466650002602504650001702530650004202547650004402589650001402633700002502647700002502672710003402697773002002731776003602751830005202787856010302839978-0-387-09724-4DE-He21320260521091821.0cr nn 008mamaa100301s2009    xxu|    s    |||| 0|eng d  a9780387097244  a997803870972447 a10.1007/978-0-387-09724-42doi  cCICY04a515.3922304a515.482231 aMeyer, Kenneth.eauthor.10aIntroduction to Hamiltonian Dynamical Systems and the N-Body Problemh[recurso electrónico] /cby Kenneth Meyer, Glen Hall, Dan Offin. 1aNew York, NY :bSpringer New York,c2009.  bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  arecurso en líneabcr2rdacarrier  atext filebPDF2rda1 aApplied Mathematical Sciences,x0066-5452 ;v900 aHamiltonian Systems -- Equations of Celestial Mechanics -- Linear Hamiltonian Systems -- Topics in Linear Theory -- Exterior Algebra and Differential Forms -- Symplectic Transformations -- Special Coordinates -- Geometric Theory -- Continuation of Solutions -- Normal Forms -- Bifurcations of Periodic Orbits -- Variational Techniques -- Stability and KAM Theory -- Twist Maps and Invariant Circle.  aThis text grew out of graduate level courses in mathematics, engineering and physics given at several universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. Topics covered include a detailed discussion of linear Hamiltonian systems, an introduction to variational calculus and the Maslov index, the basics of the symplectic group, an introduction to reduction, applications of Poincaré's continuation to periodic solutions, the use of normal forms, applications of fixed point theorems and KAM theory. There is a special chapter devoted to finding symmetric periodic solutions by calculus of variations methods. The main examples treated in this text are the N-body problem and various specialized problems like the restricted three-body problem. The theory of the N-body problem is used to illustrate the general theory. Some of the topics covered are the classical integrals and reduction, central configurations, the existence of periodic solutions by continuation and variational methods, stability and instability of the Lagrange triangular point. Ken Meyer is an emeritus professor at the University of Cincinnati, Glen Hall is an associate professor at Boston University, and Dan Offin is a professor at Queen's University. 0aMATHEMATICS. 0aGLOBAL ANALYSIS (MATHEMATICS). 0aDIFFERENTIABLE DYNAMICAL SYSTEMS. 0aMATHEMATICAL PHYSICS.14aMATHEMATICS.24aDYNAMICAL SYSTEMS AND ERGODIC THEORY.24aMATHEMATICAL AND COMPUTATIONAL PHYSICS.24aANALYSIS.1 aHall, Glen.eauthor.1 aOffin, Dan.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780387097237 0aApplied Mathematical Sciences,x0066-5452 ;v9040uhttp://dx.doi.org/10.1007/978-0-387-09724-4zVer el texto completo en las instalaciones del CICY