A First Course in Chaotic Dynamical Systems Theory
July 23, 2022 | Author: Anonymous | Category: N/A
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Vkk n`sfuss`ams, sthts, hmn hutlar prac`iks car tl`s puoi`fht`am ht7 lttps7//www.rkskhrflbhtk.mkt/puoi`fht`am/6>: F@^H^@AMV VKK Z_AC@IK
Vadk ac tlk hutlars ac tl`s puoi`fht`am hrk hisa ware`mb am tlksk rkihtkn pragkfts7
Fadpikx Nymhd`fs ac Zkrturokn Zaiymad`his S`kw pragkft
Hii famtkmt caiiaw`mb tl`s phbk whs upiahnkn oy _aokrt I. Nkvhmky Nkvhmky am am ?0 Vkptkdokr ?:?:. ^lk uskr lhs rkqukstkn kmlhmfkdkmt ac tlk nawmiahnkn c`ik.
H C`rst Faursk `m Flhat`f Nymhd`fhi Vystkds
Hnvhmfks `m Hppi`kn Dhtlkdhfs Vkr`ks Kn`tar7 Nhm`ki Ww`ii`mbkr Vtaflhsf Zhrhi N`krkmhi Kquhams, Vkfamn Kn`am Zha-I`u Flaw F_F Vthmnhrn Dhtlkdhfhi ^hoiks hmn Carduihs, 6?mn Kn`am Nhm Ww`ii`mbkr Hnvhmfkn Kmb`mkkr`mb Dhtlkdhfs w`tl DH^IHO, ^l`rn Kn`am Nkhm B. Nuy Dhreav Zrafkssks Ghdks _. E`rewaan E`re waan I`mkhr hmn @mtkbkr Apd`zham7 ^lkary hmn Zrhffk, ^l`rn Kn`am Bkrhrn V`kresdh hmn Par` Wwais @mtranufam ta C`mhmf`hi Dhtlkdhfs Ekv`m G. Lhsmbs Chst Vaivkrs car Dksl-Ohskn Fadputhams Dhf`kg Zhszymse` Nymhd`fhi Vystkds car O`aiab`fhi Danki`mb7 Hm @mtranufam
Crkn Orhukr hmn Flr`staplkr Er`os F_F Vthmnhrn Furvks hmn Vurchfks w`tl Dhtlkdht`fh®, ^l`rn Kn`am Nhv`n L. vam Vkbbkrm Lhmnoaae ac Zkr`nymhd`f Danki`mb Ciar``m Oaohru, Oaohru, Galm ^. Castkr, Zl`i`pp Zl`i`ppkk L. Bkuokiik, hmn Vtkwhrt H. V`ii`mb I`mkhr hmn Fadpikx Hmhiys`s car Hppi`fhams
Galm Z. N‐Hmbkia N‐Hm bkia Xuhnrhf Zrabrhdd`mb w`tl Fadputkr Zrabrhds D`flhki G. Okst Brkkm‐s Cumfams w`tl Hppi`fhams, Vkfamn Kn`am Nkhm B. Nuy @mtranufam ta _hnhr Hmhiys`s, Vkfamn Kn`am Ohsskd _. Dhlhczh ^lk Vkfamn-Arnkr Hnga`mt Vkms`v`ty Hmhiys`s Dktlanaiaby Nhm Bhor`ki Fhfuf` Brkkm's Cumfams w`tl Hppi`fhams, Vkfamn Kn`am Nkhm B. Nuy Apkrhams _kskhrfl7 H Zrhffhi @mtranufam, Vkfamn Kn`am D`flhki Fhrtkr, Fhd`iik F. Zr`fk, hmn Blh`tl _hohn`
Lhmnoaae ac Dkii`m ^rhmscards Pu. H. Oryfleav, A.@. Dhr`flkv, hmn M.S. Vhv`sflkmea
lps7//www.frfprkss.fad/ lps7//www. frfprkss.fad/Hnvhmfks-`m-Hppi`kn-Dhtlkdh Hnvhmfks-`m-Hppi`kn-Dhtlkdhfs/oaae-skr`ks/ fs/oaae-skr`ks/F_FHNSHZZ F_FHNSHZZD^L1 D^L1 phbk48&arnkr4puonhtk&s`zk4?>&v phbk48&arnkr4p uonhtk&s`zk4?>&v`kw4i`st&sthtus4p `kw4i`st&sthtus4puoi`slkn,cart uoi`slkn,cartlfad`mb lfad`mb
H C`rst Faursk `m Flhat`f Nymhd`fhi Vystkds ^lkary hmn Kxpkr`dkmt Vkfamn Kn`t`am
_aokrt I. Nkvhmky
F_F Zrkss ^hyiar & Crhmf`s Braup 3::: Oraekm Vaumn Zhrewhy MR, Vu`tk 6:: Oafh _htam, CI 66>? f ?:?: oy ^hyiar & Crhmf`s Braup, IIF F_F Zrkss `s hm `dpr`mt ac ^hyiar & Crhmf`s Braup, hm @mcardh ous`mkss Ma fih`d ta ar`b`mhi [.V. Bavkrmdkmt wares Zr`mtkn am hf`n-crkk phpkr @mtkrmht`amhi Vthmnhrn Oaae Mudokr-867 02 (Lhrnohfe) ^l`s oaae famth`ms `mcardht`am aoth`mkn crad hutlkmt`f hmn l`bliy rkbhrnkn saurfks. _khsamhoik karts lhvk okkm dhnk ta puoi`sl rki`hoik nhth hmn `mcardht`am, out tlk hutlar hmn puoi`slkr fhmmat hssudk rkspams`o`i`ty car tlk vhi`n`ty ac hii dhtkr`his ar tlk famskqukmfks ac tlk`r usk. ^lk hutlars hmn puoi`slkrs lhvk httkdptkn ta trhfk tlk fapyr`blt lainkrs ac hii rkpranufkn `m tl`s hmn@chpaiab`zk ta fapyr`blt lainkrs `c pkrd`ss`am tadhtkr`hi puoi`sl `m tl`s card lhs matpuoi`fht`am okkm aoth`mkn. hmy fapyr`blt dhtkr`hi lhs mat okkm hfemawiknbkn pikhsk wr`tk hmn ikt us emaw sa wk dhy rkft`cy `m hmy cuturk rkpr`mt. Kxfkpt hs pkrd`ttkn umnkr [.V. Fapyr`blt Ihw, ma phrt ac tl`s oaae dhy ok rkpr`mtkn, rkpranufkn, trhmsd`ttkn, ar ut`i`zkn `m hmy card oy hmy kikftram`f, dkflhm`fhi, ar atlkr dkhms, maw emawm ar lkrkhctkr `mvkmtkn, `mfiun`mb platafapy`mb, d`fraid`mb, hmn rkfarn`mb, ar `m hmy `mcardht`am starhbk ar rktr`kvhi systkd, w`tlaut wr`ttkm pkrd`ss`am crad tlk puoi`slkrs. Car pkrd`ss`am ta platafapy ar usk dhtkr`hi kikftram`fhiiy crad tl`s ware, pikhsk hffkss www.fapyr`blt.fad ( www.fapyr`blt.fad (lttp7//www.fapyr`blt.fad/ lttp7//www.fapyr`blt.fad/)) ar famthft tlk Fapyr`blt Fikhrhmfk Fkm-
tkr, @mf. (FFF), ??? _askwaan Nr`vk, Nhmvkrs, DH :80?6, 02
>
@dhbks crad Nymhd`fhi Vystkds . . . . . . . . . . . . . . . . H Or`kc L`stary ac Nymhd`fs . . . . . . . . . . . . . . . . . .
Kxhdpiks ac Nymhd`fhi Vystkds
?.8 ?.? ?.6 ?.> 6
`x
82
Hm Kxhdpik crad C`mhmfk . . . . . . Hm Kxhdpik crad Kfaiaby . . . . . . C`mn`mb _aat aats hmn Vaiv`mb Kquht`ams N`krkmt`hi Kquht`ams . . . . . . . . .
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Aro`ts
82 8< ?: ?? ?;
6.8 6.? 6.6 6.>
@tkrht`am . . . . . . . Aro`ts . . . . . . . . . ^yp ks ac Aro`ts . . . Atlkr Aro`ts . . . . .
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?; ?3 ?2 6:
6.; 6.3
^lk Nauoi`mb Cumft`am . . . . . . . . . . . . . . . . . . . . . Kxpkr`dkmt7 ^lk Fadputkr Dhy I`k . . . . . . . . . . . . .
68 66
Brhpl`fhi Hmhiys`s
62
>.8 >.?
62 60
Brhpl`fhi Hmhiys`s . . . . . . . . . . . . . . . . . . . . . . . . Aro`t Hmhiys`s . . . . . . . . . . . . . . . . . . . . . . . . . .
>.6 ;
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C`xkn hmn Zkr`a n`f Za`mts
;.8 ;.? ;.6 ;.> ;.; ;.3 3
^lk Zlhsk Zartrh`t
>8 >;
H C`xkn Za`mt ^lkarkd . . . . . . Httrhft`am hmn _kpuis`am . . . . . Fhifuius ac C`xkn Za`mts . . . . . Rly @s ^l`s ^ruk1 . . . . . . . . . Zkr`an`f Za`mts . . . . . . . . . . . Kxpkr`dkmt7 _htks ac Famvkrbkmfk
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>; >3 >2 ;: ;; ;2
O`curfht`ams
38
3.8 3.?
38 3;
Nymhd`fs ac tlk Xuhnrht`f Dhp . . . . . . . . . . . . . . . . ^lk Vhnnik-Mank O`curfht`am . . . . . . . . . . . . . . . . . .
v
v`
3.6 3.> 2
0
^lk Zkr`an an--Nauoi`mb O`curfht`am . . . . . . . . . . . . . . . . Kxpkr`dkmt7 ^lk ^rhms`t`am ta Flhas . . . . . . . . . . . . .
^lk Xuhnrht`f Chd`iy
2. 2.88 2.? 2.6 <
Famtkmts
30 26 20
^l ^lkk Fh Fhsk sk f 4 ∟? . . . . . . . . . . . . . . . . . . . . . . . . . ^lk Fhsk f 9 ‖? . . . . . . . . . . . . . . . . . . . . . . . . . ^lk Fhmtar D`nnik-^l`rns Vkt . . . . . . . . . . . . . . . . .
20 2
88.> Vuosl`cts ac C`m`tk ^yp k . . . . . . . . . . . . . . . . . . . . . 8? _aik ac tlk Fr`t`fhi Za`mt
8;8 8;0
8?.8 ^lk Vflwhrz`hm Nkr`vht`vk . . . . . . . . . . . . . . . . . . . 8?.? Fr Fr`t `t`f `fhhi Za`m `mtts hmn Ohs`ms ac Httrhft` ft`am . . . . . . . . . . . . 86 Mkwtam‐s Dktla n
8;0 83? 830
86.8 Oh O hs`f Zrap krt`ks . . . . . . . . . . . . . . . . . . . . . . . . .
830
86.? Famvkrbkmfk hmn Mamfamvkrbkmfk
826
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8> Crhfthis
8>.8 ^l ^ lk Flhas Bhdk . . . . 8>.? ^lk Fhmtar Vkt _kv`s`tkn 8>.6 ^lk V`krp`mse` ^r`hmbik . 8>.> ^lk V`krp`mse` Fhrpkt . . 8>.; ^lk Ea fl Vmawhek . . . ^ap aiab`fhi N`dkms`am . 8>.3 ^a
8 .0 8>.8:
v``
Crhfthi N`dkms`am . . . . . . . . . . . @tkrhtkn Cumft`am Vystkds . . . . . . . Kx Kxpk pkrr`d `dkm kmtt7 C` C`m mn tlk @t @tkr krht htkn kn Cumft umft`a `am m Kx Kxpk pkrr`dkmt7 H ’_khi— Flhas Bhdk . .
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8; Fadpikx Cumft`ams
8;.8 8;.? 8;.6 8;.>
Fadpikx Hr`tldkt`f . . . . . . Fadpikx Vquhrk _a ats . . . . I`mkhr Fadpikx Cumft`ams . . Fhifuius ac Fadpikx Cumft`ams
?88
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83 ^lk Gui`h Vkt
83.8 83.? 83.6 83.> 83.; 83 .; 83.3
^lk Vquhr`mb Cumft`am . . . . . . . . . . . . . . Hm Hmaatlkr Flhat`f Xuhnrht`f Cumft`am . . . . . . Fhmtar Vkts Hbh`m . . . . . . . . . . . . . . . . . Fadput`mb tlk C`iikn Gui`h Vkt . . . . . . . . . . Kx Kxpkr pkr`d `dkm kmt7 t7 C` C`ii iikn kn Gu Gui` i`hh Vkts Vkts hmn hmn Fr Fr`t `t`f `fhi hi Ar Aro` o`ts ts ^lk Gui`h Vkt hs h _kpkiikr . . . . . . . . . . . . ^lk Cumnhdkmthi N`flatady . . . . . . ^lk Dhmnkiorat Vkt . . . . . . . . . . . Fadpikx O`curfht`ams . . . . . . . . . . Kxpk pkrr`dkmt7 Zkr`an anss ac tlk Ouios . . .
?88 ?8; ?8< ??: ??0
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82 ^lk Dhmnkiorat Vkt
82.8 82.? 82.6 82.>
80> 802 ?: ?:>> ?:;
??0 ?66 ?6; ?>: ?> ?>;; ?>3 ?;8
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?;8 ?;> ?;2 ?36
8822..3; 82.2 82.< 82 .<
Kx Kxpk pkr dkkm mtt77 K xp krr``d Kxpk pkrr`dkmt7 Kx Kxpkr pkr`d `dkm kmt7 t7
Zkarw`an ans acntnlk .Atl At L tas H . l. kr. O . u. io . s. .. .. .. .. .. .. .. .. .. .. .. .. C`mn tlk Gui`h Vkt . . . . . . . . . . . . . . . . . V V`d `d`ih `ihr`t r`ty y ac tlk tlk Dhmn Dhmnki kior orat at Vk Vktt hmn hmn Gu Gui` i`hh Vkts Vkts
8< Atlkr Fadpikx Nymhd`fhi Vystkds
8. @c wk `mvkst`bhtk kxpamkmt`hi cumft`ams ac tlk card card f kxp( kxp(zz ), wk mn Gui`h skts tlht iaae qu`tk n`krkmt hs, car kxhdpik, `m Zihtk `m Zihtk 83. 83. Hmn wk fhm hisa iaae ht tlk phrhdktkr pihmks (tlk f-pihmks) car tlksk dhps, h part`am ac wl`fl `s slawm `m Zihtk 82. 82. @m hn hnn` n`t` t`am am,, wk lh lhv vk rk rkckr ckrkm kmfkn fkn h mud udokr okr ac am ami`m i`mkk v` v`nk nkas as pas pastk tkn n am dy wko kos` s`tk tk tl tlht ht w` w`ii ii hi hiia iaw w yau ta sk skkk tl tlkk nr nrhd hdht ht`f `f flh lhmb mbks ks tl tlks kskk sy sysstkds tk ds um umnk nkrb rbaa hs ph phrh rhdk dktk tkrs rs vhr hry y. Hi Hiii ac tl tlks kskk v` v`nk nkas as hr hrkk hvh` h`ih ihoi oikk ht dhtl.ou.knu/NPVPV/hm`dh dhtl.ou.knu/ NPVPV/hm`dht`ams.ltdi t`ams.ltdi. ^lk `dhbks `m tl`s dhtlkdht`fhi taur slaw qu`tk fikhriy tlk brkht okhuty ac dhtlkdht`fhi nymhd`fhi systkds tlkary. Out wlht na tlksk p`fturks dkhm m
m
hmn wly hrk `dparthmt1 ^lksk hrk qukst`ams tlht wk w`ii hnnrkss `m tlk rkdh`mnkr ac tlky tl`s oaae.
8.? 8. ?
H Or` Or`kc kc L`s L`sta tary ry ac N Nym ymhd hd`f `fss
Nymhd`fhi systkds lhs h iamb hmn n`st`mbu`slkn l`stary hs h orhmfl ac dhtlkdht`fs. Okb`mm`mb w`tl tlk cumnhdkmthi ware ac @shhf Mkwtam, n`krkmt`hi kquht`ams okfhdk tlk pr`mf`phi dhtlkdht`fhi tkflm`quk car nksfr`o`mb prafkssks tlht kvaivk famt`muausiy `m t`dk. @m tlk k`bltkkmtl hmn m`mktkkmtl fkmtur`ks, dhtlkdht`f`hms nkv`skn mudkraus tkflm`quks car saiv`mb n`krkmt`hi kquht`ams kxpi`f`tiy. ^lksk dktlans `mfiunkn Ihpihfk trhmscards, pawkr skr`ks saiut`ams, vhr`ht`am ac phrhdktkrs, i`mkhr hibkorh`f dktlans, hmn dhmy atlkr tkflm`quks chd`i`hr crad h ohs`f umnkrbrhnuhtk faursk `m arn`mhry n`krkmt`hi kquht`ams. ^lkrk whs amk dhgar hw `m tl`s nkvkiapdkmt. S`rtuhiiy hii ac tlk hmhiyt`f tkflm`quks car saiv`mb n`krkmt`hi kquht`ams warekn dh`miy car i`mkhr n`krkmt`hi kquht`ams. Mami`mkhr n`krkmt`hi kquht`ams pravkn dufl dark n`stfuit ta saivk. [mcartumhtkiy, dhmy ac tlk dast `dparthmt prafkssks `m mhturk hrk `mlkrkmtiy mami`mkhr. Hm kxhdpik ac tl`s `s prav`nkn oy Mkwtam‐s ar`b`mhi dat`vht`am car nkvkiap`mb fhifuius hmn n`krkmt`hi kquht`ams. Mkwtam‐s ihws kmhoik ta wr`tk nawm tlk kquht`ams tlht nksfr`ok tlk dat`am ac tlk pihmkts `m tlkussaihr systkd, hdamb dhmy atlkr `dparthmt plys`fhi plkmadkmh. Emawm hs tlk m tlk m-oany -oany praoikd, tlksk ihws b`vk us h systkd ac n`krkmt`hi kquht`ams wlask saiut`ams
H Or`kc L`stary ac Nymhd`fs
;
nksfr`ok tlk dat`am ac ac m ’pa`mt dhssks— dav`mb `m sphfk suogkft amiy ta tlk`r awm dutuhi brhv`tht`amhi httrhft`am. @c wk emaw tlk `m`t`hi pas`t`ams hmn vkiaf`t`ks ac tlksk dhssks, tlkm hii wk lhvk ta na `s saivk Mkwtam‐s n`krkmt`hi kquht`am ta ok hoik ta prkn`ft wlkrk hmn law tlksk dhssks w`ii davk `m tlk cuturk. ^l`s turms aut ta ok h card`nhoik thse. @c tlkrk hrk amiy amk ar twa pa`mt dhssks, tlkm tlksk kquht`ams dhy ok saivkn kxpi`f`tiy, hs `s actkm namk `m h crksldhm ar sapladark fhifuius ar plys`fs fihss. Car tlrkk ar dark dhssks, tlk praoikd tanhy rkdh`ms fadpiktkiy umsaivkn, nksp`tk tlk karts ac faumtikss dhtlkdht`f`hms avkr tlk phst tlrkk fkmtur`ks. @t `s truk tlht mudkr`fhi saiut`ams ac n`krkmt`hi kquht`ams oy fadputkrs lhvk hiiawkn us ta hpprax`dhtk tlk oklhv`ar ac tlk hftuhi saiut`ams `m dhmy fhsks, out tlkrk hrk st`ii rkb`dks `m tlk m tlk m-oany -oany praoikd wlkrk tlk saiut`ams hrk sa fadpi`fhtkn ar flhat`f tlht tlky nkcy kvkm mudkr`fhi fadputht`am. Hitlaubl tlk kxpi`f`t saiut`am ac mami`mkhr arn`mhry n`krkmt`hi kquht`ams lhs pravkn kius`vk, tlkrk lhvk okkm caur ihmndhre kvkmts avkr tlk phst 86: ykhrs tlht lhvk rkvaiut`am`zkn tlk why wk stuny nymhd`fhi systkds. Zkrlhps tlk dast `dparthmt kvkmt affurrkn `m 8 phpkr U6: 6:TT, Aikeshmnr Vlhreavsey nktkrd`mkn tlht, `c sufl h dhp am tlk rkhi i`mk lhn h fyfik ac pkr`an m,
tlkm lk fauin i`st kxhftiy hii ac tlk atlkr pkr`ans tlht sufl h dhp dust
H Or`kc L`stary ac Nymhd`fs
2
lhvk. [mcartumhtkiy, tl`s phpkr whs puoi`slkn `m [erhm`hm hmn lkmfk whs mat emawm ht hii `m tlk wkst. Lawkvkr, hctkr tlk I`-Parek phpkr hppkhrkn, tl`s rksuit okfhdk amk ac tlk dast `mtkrkst`mb `m dankrm nymhd`fhi systkds tlkary. Hii ac tlksk rksuits hrk nksfr`okn `m Flhptkr `m Flhptkr 88. 88. ^lksk iknhmn ta hkmb`mkkr`mb trkdkmnaus`murry ac hft`v`ty `m mami`mkhr nymhd`fs `m hii hrkhshnvhmfks ac sf`kmfk tlk kmsu`mb nkfhnk. Car kxhdpik, tlk kfaiab`st _aokrt Dhy caumn tlht vkry s`dpik `tkrht`vk prafkssks tlht hr`sk `m dhtlkdht`fhi o`aiaby fauin pranufk `mfrkn`oiy fadpikx hmn flhat`f oklhv`ar. ^lk plys`f`st D`tflkii Ck`bkmohud, ou`in`mb am Vdhik‐s khri`kr ware, mat`fkn tlht, nksp`tk tlk fadpikx`ty ac flhat`f oklhv`ar, tlkrk whs sadk skdoihmfk ac arnkr `m tlk why systkds okfhdk flhat`f. Zlys`f`sts Lhrry Vw`mmky hmn Gkrry Baiiuo slawkn tlht tlksk dhtlkdht`fhi nkvkiapdkmts fauin hftuhiiy ok aoskrvkn `m plys`fhi hppi`fht`ams, mathoiy `m turouikmt u`n aw. Ihtkr, atlkr systkds, sufl hs tlk dat`am ac tlk cardkr pihmkt Ziuta ar tlk okht ac tlk ludhm lkhrt, lhvk okkm slawm ta kxl`o`t s`d`ihr flhat`f phttkrms. @m dhtlkdht`fs, dkhmwl`ik, mkw tkflm`quks wkrk nkvkiapkn ta lkip umnkrsthmn flhas. Galm Bufekmlk`dkr hmn _aokrt C. R`ii`hds kdpiaykn tlk tlkary ac strhmbk httrhftars ta kxpih`m tlk plkmadkmam tlht Iarkmz lhn aoskrvkn h nkfhnk khri`kr. Hmn taais sufl hs tlk Vflwhrz`hm nkr`vht`vk, sydoai`f nymhd`fs, hmn o`curfht`am tlkary„hii tap`fs wk w`ii n`sfuss `m tl`s oaae„wkrk slawm ta pihy hm `dparthmt raik `m umnkrsthmn`mb tlk oklhv`ar ac nymhd`fhi systkds. ^lk caurtl hmn dast rkfkmt dhgar nkvkiapdkmt `m nymhd`fhi systkds whs tlk hvh`iho`i`ty ac l`bl-spkkn fadput`mb hmn, `m phrt`fuihr, fadputkr brhpl`fs. Carkdast hdamb tlk fadputkr-bkmkrhtkn rksuits whs Dhmnkiorat‐s n`sfavkry `m 807 ^lrkk hmn caur-khrkn rhoo`t Gui`h skts.
0
Zihtk ;7 H nkmnr`tk hmn h Fhmtar skt Gui`h skt.
8:
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