LEADER 03250nam 22004575a 450 001 9910151932103321 005 20100519234500.0 010 $a3-03719-581-9 024 70$a10.4171/081 035 $a(CKB)3710000000953854 035 $a(CH-001817-3)113-100519 035 $a(PPN)178155748 035 $a(EXLCZ)993710000000953854 100 $a20100519j20100519 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLectures on Dynamical Systems$b[electronic resource] $eHamiltonian Vector Fields and Symplectic Capacities /$fEduard Zehnder 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2010 215 $a1 online resource (363 pages) 225 0 $aEMS Textbooks in Mathematics (ETB) 330 $aThis book originated from an introductory lecture course on dynamical systems given by the author for advanced students in mathematics and physics at the ETH Zurich. The first part centres around unstable and chaotic phenomena caused by the occurrence of homoclinic points. The existence of homoclinic points complicates the orbit structure considerably and gives rise to invariant hyperbolic sets nearby. The orbit structure in such sets is analyzed by means of the shadowing lemma, whose proof is based on the contraction principle. This lemma is also used to prove S. Smale's theorem about the embedding of Bernoulli systems near homoclinic orbits. The chaotic behavior is illustrated in the simple mechanical model of a periodically perturbed mathematical pendulum. The second part of the book is devoted to Hamiltonian systems. The Hamiltonian formalism is developed in the elegant language of the exterior calculus. The theorem of V. Arnold and R. Jost shows that the solutions of Hamiltonian systems which possess sufficiently many integrals of motion can be written down explicitly and for all times. The existence proofs of global periodic orbits of Hamiltonian systems on symplectic manifolds are based on a variational principle for the old action functional of classical mechanics. The necessary tools from variational calculus are developed. There is an intimate relation between the periodic orbits of Hamiltonian systems and a class of symplectic invariants called symplectic capacities. From these symplectic invariants one derives surprising symplectic rigidity phenomena. 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E. Jorgenson and Joseph P. Veres 210 1$aCleveland, Ohio :$cNational Aeronautics and Space Administration, Glenn Research Center,$dMarch 2020. 215 $a1 online resource (102 pages) $cillustrations (some color) 225 1 $aNASA/TM ;$v2020-220457 300 $a"March 2020." 320 $aIncludes bibliographical references (page 102). 517 $aCOMDES-MELT 606 $aComputer programs$2nasat 606 $aFailure modes$2nasat 606 $aMoisture content$2nasat 606 $aTurbofan engines$2nasat 606 $aReal time operation$2nasat 615 7$aComputer programs. 615 7$aFailure modes. 615 7$aMoisture content. 615 7$aTurbofan engines. 615 7$aReal time operation. 700 $aJorgenson$b Philip C. 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