
sinai-ruul-bowen mojmap

ergodic siddhantachya ganiteey shakhet, sinai-ruel-bowen (ess. aar. bii.) mojmap heey eka aparivartaniy mojmap aahe jeey tyach prakare vagate, parantu teey ergodic mojmap nahee. ergodic honyasathi, vel sarasari hii jawaljawal serve prarambhik avasthansathi jaaga sarasarichya barobarichi asane aavashyak aahe, sootra _ 1, sootra _ 2 hii fages space aahe. ess. aar. bii. mojamapachya sootra _ 3 sathee, sakaratmak lebsgue mojamapachya sanch sootra _ 4 madheel prarambhik avasthansathi ergodicity sthitee vaidh asane purese aahe.
ess. aar. bii. upayanshi sambandhit prarambhik kalpana yakov sinai, david ruel aanee rufus bowen yanni anosov defiomorphism aanee svayamsiddha aakarshakanchya qamee samanya kshetrat sadar kelya.
vyakhya.
sootra _ 5 haah nakasha asoo dya. mug sootra _ 2 varr paribhashit kelele mapan sootra _ 3 heey sakaratmak lebsgue mojamapache sootra _ 8 astitvat asalyas aanee tyach lebsgue mojmapasah sootra _ 9 asalyas ess. aar. bii. mojmap aahe, jase keeh
pratyek sutrasathi _ 11 aanee pratyek nirantar karya sutrasathi _ 12.
ess. aar. bii. mojamapache sootra _ 3 heey asey eka sootra mhanoon pahile jaau shakate jeey sootra _ 2 madhye asalelya lahan sanchavar berkhoffchya ergodic pramey nishkarshanche samadhan karate.
ess. aar. bii. upayanche astitva.
khaleel pramey ess. aar. bii. upayanchya astitvasathi puresha atty sthapit karate. teey svayamsiddhatechya prakaranala eka aakarshan manato, jeey sope aahe, parantu teey adhik samanya paristhitiparyant vistarit kele gele aahe.
pramey 1: sootra _ 15 heey eka sootra _ 16 bhinnarupata asoo dya, jyat eka svayamsiddha eka aakarshak sootra _ 17 aahe. asey gruheet dhara qee haah aakarshak 'irreducible' aahe, mhanje, heey sootra _ 18 antargat aparivartaniy asalelya itar done sanchanche millen nahee. mug eka adviteey borelian mojmap sootra _ 3 aahe, sootra _ 20 saha, jeey khaleel samatulya vidhananni darshavile aaheh
tasech, yaa paristhitit sootra _ 27 hii eka mapan-sanrakshn karnari gatishil pranali aahe.
heey dekhil siddha jhaale aahe qee vareel sootra _ 3 heey markov sakhalichya shoonya-dhwani maryadechya sthir vitaranachya barobariche aahe, jyache steet sootra _ 29 aahe. mhanjech, pratyek bindu sootra _ 1 heey noise level sootra _ 32 saha sankraman sambhavyata sootra _ 31 shhee sambandhit aahe, jeey pudhil sthitichya anishchitateche praman asha prakare mojate keeh
jethe sootra _ 34 heey diarac mojmap aahe. shoonya-dhwani maryada mhanje jevha dhwani patali shoonyachya jawal jaate tevha yaa markov sakhaliche sthir vitaran. yache mahatva asey aahe qee teey ganitiyadrushtya sangate qee ess. aar. bii. mojmap heey vyavharik prakarananmadhye eka "changle" andaje aahe jethe qamee pramanat aavaj astitvat aahe, jaree sahan karnyayogya asalelya aavajachya pramanabaddal kahihi sangitale jaau shakat nahee.