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(1)Marie. Aubry. Sets. M compact. L TM SIR. All. in M. curves. Tonelli Lag cont. abs. Recap r. B. Kalb. M. ni. glob. A Glas. min. for L if. min. Adr. T. aß IM. Hat 0lb. a. V D SM kack. is. time free. All rfca.gl. mei r a. tune forenni global. Marie x. geh. 0. mi. Au. gr. x. M. y. gelb. mei. global. Ltk. Cit T. Ir. 5lb. a. Lj. for. global. r. Potential T. d b. p. for L. mi. Hb. rein. Keck. for. Value. Er. 0. g. x. O. TJ MI HTT.

(2) this. Def. x. T. y. er is. actually. a. min. Analrt. inf. YEAH g x. Info Pulley. y. is. for. T. this also. k. 42. anni a. When. If. is. lqcx.gl. I TSO. then. d. For. 1. An. lt. Auch. u. 0 o. o. x. all. dünn Where. G 4. ge. als. g Prog. o. ULI. Marie. geh. x. to. C. K2. Sup h ait. have. if if. I J. h k. EM. ccc L. z. T. 0. with etwa Irl rebel. y cGK.nl 0.

(3) Moreover. for. k. da 1. du. R. 1. si. Lipschitz OHHH for k. tolly. Aubry. Marie. sets. Answer to. Kl. x n. metrei. For. We. by. can. there. are. What gr. D. Kalb. da. mi. happen. M. ni. at semi. ctu.fr ca.sg i e. The. y. tame. Marie. x. pseudo. h. sell. if if. y. two. any. min. no. if. yes. connect. time free. a. Df. ni. a. k yell. L. have. x.y.CM. is. of. T. so. pts in µ. energy. for h. F. h. du. kack CCC. static. for. Lif. 9ulHat.rlbD. free. min. set. is. for Lte. L.

(4) Ü. ETMIJ. ul. x. atie. tecRs.th.x rHI jHI yseni.ee. v. Note. N. Ü. is. invariat. is. closed. Recall. 0dL. Han. Antritt x. If Facts. Z. y. yl. An i. e. Hb. A. static. lv ca.gI Yi. k. and. rlb. day. The. Aubry Set. Ä. lx.ci. Th. echt. daalrlbI.rlall. day ylal.pl b e. flat. for L of. static. semi. flow. alt for. is. El. b. r. daly. D IM. y. al. the. under. in. 17. Hat. static. Iten t. v. JA.

(5) Note. Ä. is. invariant. Ä. is. closed. Ä For x. TM. c. u. y. set. w. TM. e. 74. I. and w. G. x u. Th l. C. w. Let. e. r. x. Ä and. y. w. E. Ü. iff. G wt. with tu. Gla. Gew. Then. 0. I only. Prop. ht. effx.nl. s.ae. AT Ä. xlx.DE u. Ü. with tn. 7ft and. 2. flow. limits. w. u. x. EL. EN. and. a. oder. Ew. yfnlx.ch. x. u. y w. with. tm. s.K.tn. so.

(6) 4. In. Ttt y. ix. 4. i. 44 T. Tv show. Alte. o. 0. 461,4C s. 41 es. c. jlt.tt. t y. implies. Hs. to check. Ju. w. static. y. Enough. y. static. semi. y. e. T. 5. 4. DEN. Dante. Ttt. u. x. se. w. Igs. c. uniqueness. E. F. µ. of. Tlc. 0. EL sol some. without. Alten bin. 0dL. 41ns. Alta. les. bin. MIS. yl. s. n. Vultuten. l. s.

(7) hin AL.cm. ktEs.s. Alten Hutes. bin hin. Alten KIES. legitimen. bin hin. yt. Def. yt. s. s. tm.tn. s. rnltm.tn sl. KH. hi hi da Non. tut. KH. Vwl. s. 0. s. D. wandering points. Yt. X. if HU. X. flow mbh. EX u. 0. 0 f UI nu Write Sha c X I x non Facts MX wlxIESLleIV. non. I. wandes. tsns.lk. wandering xeX.

(8) e. Dhikr. E. Inclusion. can. Consider. the pendulum. Ä. t. sein 0. be. Ä. need. weal. KAMI. proper. 0. Ö. e 0 non vor. Marie t. X. wandering w limits. pt. which. are. neither. Lagrangian E. TTM. vector. field. er. 2.

(9) Define. where Hill. from. comes. X. Graph X. M. Also. yea. semi. of. curves. Xcx. 141. SO. Nra. eben. 0. X. are. time free. for Lx. Ä. Graph X. 44. turns out is true. static. GraphIN IT. 5. M. This. v. Htt. Tl It. TM I. e. x u. IKEA. metric. IGraphai. integral mir. x. Riem. a. krank d. SR. TM. Lag. a. tht. because. s. µ. Graphik. integral. curves. VK.nl are.

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