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. This allows a first glimpse of the fast developing new field of symplectic topology. 606 $aCalculus of variations$2bicssc 606 $aDynamical systems and ergodic theory$2msc 606 $aOrdinary differential equations$2msc 606 $aDifferential geometry$2msc 606 $aMechanics of particles and systems$2msc 615 07$aCalculus of variations 615 07$aDynamical systems and ergodic theory 615 07$aOrdinary differential equations 615 07$aDifferential geometry 615 07$aMechanics of particles and systems 686 $a37-xx$a34-xx$a53-xx$a70-xx$2msc 700 $aZehnder$b Eduard$042588 801 0$bch0018173 906 $aBOOK 912 $a9910151932103321 996 $aLectures on Dynamical Systems$92565663 997 $aUNINA LEADER 02675oam 2200781 450 001 9910709724803321 005 20180828112417.0 035 $a(CKB)5470000002473001 035 $a(OCoLC)761197631 035 $a(OCoLC)995470000002473001 035 $a(EXLCZ)995470000002473001 100 $a20111115j198604 ua 0 101 0 $aeng 135 $aurun||||a|a|| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStatic investigation of two STOL nozzle concepts with pitch thrust-vectoring capability /$fMary L. Mason and James R. Burley II 210 1$aWashington, D.C. :$cNational Aeronautics and Space Administration, Scientific and Technical Information Branch,$dApril 1986. 215 $a1 online resource (54 pages) $cillustrations 225 1 $aNASA/TP ;$v2559 300 $a"April 1986." 320 $aIncludes bibliographical references (pages 13-14). 606 $aNozzle geometry$2nasat 606 $aStatic tests$2nasat 606 $aNozzle thrust coefficients$2nasat 606 $aAxisymmetric flow$2nasat 606 $aAfterburning$2nasat 606 $aJet nozzles$xTesting 606 $aAirplanes$xMotors$xThrust 606 $aPitching (Aerodynamics) 606 $aShort take-off and landing aircraft 606 $aAirplanes$xMotors$xThrust$2fast 606 $aJet nozzles$xTesting$2fast 606 $aPitching (Aerodynamics)$2fast 606 $aShort take-off and landing aircraft$2fast 608 $aOnline resources. 615 7$aNozzle geometry. 615 7$aStatic tests. 615 7$aNozzle thrust coefficients. 615 7$aAxisymmetric flow. 615 7$aAfterburning. 615 0$aJet nozzles$xTesting. 615 0$aAirplanes$xMotors$xThrust. 615 0$aPitching (Aerodynamics) 615 0$aShort take-off and landing aircraft. 615 7$aAirplanes$xMotors$xThrust. 615 7$aJet nozzles$xTesting. 615 7$aPitching (Aerodynamics) 615 7$aShort take-off and landing aircraft. 700 $aMason$b Mary L.$01407755 702 $aBurley$b James R. 712 02$aUnited States.$bNational Aeronautics and Space Administration.$bScientific and Technical Information Branch, 712 02$aLangley Research Center. 801 0$bOCLCE 801 1$bOCLCE 801 2$bOCLCQ 801 2$bOCLCF 801 2$bOCLCQ 801 2$bOCLCO 801 2$bOCLCQ 801 2$bGPO 801 2$bMERUC 801 2$bGPO 906 $aBOOK 912 $a9910709724803321 996 $aStatic investigation of two STOL nozzle concepts with pitch thrust-vectoring capability$93506423 997 $aUNINA