LEADER 05085nam 2200661Ia 450 001 9910782274103321 005 20230607222141.0 010 $a1-281-95639-2 010 $a9786611956394 010 $a981-281-076-5 035 $a(CKB)1000000000538133 035 $a(EBL)1679288 035 $a(OCoLC)881611083 035 $a(SSID)ssj0000254705 035 $a(PQKBManifestationID)11207024 035 $a(PQKBTitleCode)TC0000254705 035 $a(PQKBWorkID)10209245 035 $a(PQKB)10155834 035 $a(MiAaPQ)EBC1679288 035 $a(WSP)00001349 035 $a(Au-PeEL)EBL1679288 035 $a(CaPaEBR)ebr10255566 035 $a(CaONFJC)MIL195639 035 $a(EXLCZ)991000000000538133 100 $a20020701d2001 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSymplectic twist maps$b[electronic resource] $eglobal variational techniques /$fChristophe Gole? 210 $aSingapore ;$aRiver Edge, NJ $cWorld Scientific$dc2001 215 $a1 online resource (324 p.) 225 1 $aAdvanced series in nonlinear dynamics ;$vv. 18 300 $aDescription based upon print version of record. 311 $a981-02-0589-9 320 $aIncludes bibliographical references (p. [293]-301) and index. 327 $aContent ; Foreword ; 0 Introduction ; 1 Fall from Paradise ; 2 Billiards and Broken Geodesies ; 3 An Ancestor of Symplectic Topology ; 1 Twist Maps of the Annulus ; 4 Monotone Twist Maps of the Annulus ; 5 Generating Functions and Variational Setting ; 6 Examples 327 $a7 The Poincare-Birkhoff Theorem 2 The Aubry-Mather Theorem ; 8 Introduction ; 9 Cyclically Ordered Sequences And Orbits ; 10 Minimizing Orbits ; 11 CO Orbits Of All Rotation Numbers ; 12 Aubry-Mather Sets ; 3 Ghost Circles ; 13 Appendix: Cyclically Ordered Sequences and Circle Maps 327 $a14 Gradient Flow of the Action 15 The Gradient Flow and the Aubry-Mather Theorem ; 16 Ghost Circles ; 17 Construction of Ghost Circles ; 18 Construction of Disjoint Ghost Circles ; 19 Proof of Lemma 18.5 ; 20 Proof of Theorem 18.1 ; 21* Remarks and Applications 327 $a22 Proofs of Monotonicity and of the Sturmian Lemma 4 Symplectic Twist Maps ; 23 Symplectic Twist Maps of Tn x Rn ; 24 Examples ; 25 More on Generating Functions ; 26 Symplectic Twist Maps on General Cotangent Bundles of Compact Manifolds 327 $a5 Periodic Orbits for Symplectic Twist Maps of T*Tn 27 Presentation Of The Results ; 28 Finite Dimensional Variational Setting ; 29 Second Variation and Nondegenerate Periodic Orbits ; 30 The Coercive Case ; 31 Asymptotically Linear Systems ; 32 Ghost Tori 327 $a33 Hyperbolicity Vs. Action Minimizers 330 $a This book concentrates mainly on the theorem of existence of periodic orbits for higher dimensional analogs of Twist maps. The setting is that of a discrete variational calculus and the techniques involve Conley-Zehnder-Morse Theory. They give rise to the concept of ghost tori which are of interest in the dimension 2 case (ghost circles). The debate is oriented somewhat toward the open problem of finding orbits of all (in particular, irrational) rotation vectors.
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