10 research outputs found

    Rabinowitz Floer homology and coisotropic intersections

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    ํ•™์œ„๋…ผ๋ฌธ (๋ฐ•์‚ฌ)-- ์„œ์šธ๋Œ€ํ•™๊ต ๋Œ€ํ•™์› : ์ˆ˜๋ฆฌ๊ณผํ•™๋ถ€, 2014. 2. Urs Frauenfelder.Urs Frauenfelder์™€ Kai Cieliebak์€ Paul Rabinowitz๊ฐ€ ์ž์œจ์  ํ•ด๋ฐ€ํ„ด ์‹œ์Šคํ…œ์—์„œ ์ฃผ๊ธฐ๊ถค๋„๋“ค ์ฐพ๊ธฐ ์œ„ํ•ด ์ œ์•ˆํ•œ ๋ผ๊ทธ๋ž‘์ฆˆ ์Šน์ˆ˜ ํ•จ์ˆ˜๋ฅผ ์‚ฌ์šฉํ•˜์—ฌ Rabinowitz Floer homology ์ด๋ก ์„ ๊ฐœ๋ฐœํ•˜์˜€๋‹ค. ์ด ๋…ผ๋ฌธ์—์„œ๋Š” ์šฐ๋ฆฌ๋Š” ์ž„์˜์˜ ์—ฌ์ฐจ์›์„ ๊ฐ€์ง€๋Š” ์—ฌ๋“ฑ๋ฐฉ์„ฑ ๋ถ€๋ถ„๋‹ค์–‘์ฒด ์œ„์˜ ์—ญํ•™๊ตฌ์กฐ๋ฅผ ๋ถ„์„ํ•˜๋Š”๋ฐ ์ ํ•ฉํ•œ ์—ฌ๋Ÿฌ๊ฐœ์˜ Lagrange ์ƒ์ˆ˜๋“ค์„ ๊ฐ€์ง€๋Š” ์ผ๋ฐ˜ํ™”๋œ Rabinowitz ํ•จ์ˆ˜๋ฅผ ์—ฐ๊ตฌํ•  ๊ฒƒ์ด๋‹ค. ์šฐ๋ฆฌ๋Š” ์ผ๋ฐ˜ํ™”๋œ Rabinowitz ํ•จ์ˆ˜๋ฅผ ์‚ฌ์šฉํ•˜์—ฌ ์—ฌ๋“ฑ๋ฐฉ์„ฑ ๊ถค์  ๊ต์ฐจ์ , ์—ฌ๋“ฑ๋ฐฉ์„ฑ ๋ถ€๋ถ„ ๋‹ค์–‘์ฒด์˜ ์ „์น˜๊ฐ€๋Šฅ์„ฑ, ๊ทธ๋ฆฌ๊ณ  ์—ฌ๋“ฑ๋ฐฉ์„ฑ ๋ถ€๋ถ„๋‹ค์–‘์ฒด์˜ Rabinowitz Floer homology ๋“ฑ์— ๊ด€ํ•ด ์—ฐ๊ตฌํ•  ๊ฒƒ์ด๋‹ค. ์šฐ๋ฆฌ๋Š” ๋˜ํ•œ Rabinowitz Floer homology์˜ Kรผnneth ๊ณต์‹์„ ์œ ๋„ํ•˜์—ฌ ๋ฌดํ•œ๊ฐœ์˜ ์—ฌ๋“ฑ๋ฐฉ ๊ถค์  ๊ต์ฐจ์ ์„ ๊ฐ€์ง€๋Š” ์—ฌ๋“ฑ๋ฐฉ์„ฑ ๋ถ€๋ถ„๋‹ค์–‘์ฒด๋“ค์„ ์ฐพ์„ ๊ฒƒ์ด๋‹ค. ์ด ์—ฐ๊ตฌ๋Š” ์—ฌ๋Ÿฌ ๊ฐœ์˜ ์šด๋™ ์ƒ์ˆ˜ (๋ณด์กด๋Ÿ‰) ๋ฅผ ๊ฐ€์ง€๋Š” ์šด๋™ ์‹œ์Šคํ…œ์„ ์—ฐ๊ตฌํ•˜๋Š”๋ฐ ์ค‘์š”ํ•œ ์—ญํ• ์„ ํ•  ๊ฒƒ์ด๋‹ค.Rabinowitz Floer homology theory was developed by Kai Cieliebak and Urs Frauenfelder using a Lagrange multiplier action functional, which was introduced by Paul Rabinowitz in order to detect periodic orbits of autonomous Hamiltonian systems. In this thesis, we study a generalized Rabinowitz action functional with several Lagrange multipliers, which is well suited for exploring dynamics on coisotropic submanifolds of arbitrary codimensions. Using this, we investigate among others, the existence problem of leafwise coisotropic intersection points, displaceability of coisotropic submanifolds, and Rabinowitz Floer homology for coisotropic submanifolds. We also derive a Kรผnneth formula for the Rabinowitz Floer homology of product coisotropic submanifolds, and this enables us to find a class of coisotropic submanifolds which have infinitely many leafwise coisotropic intersection points. This study will serve as a crucial tool for exploring autonomous dynamical systems with several integrals.Abstract i 1 Preliminaries on symplectic geometry 1 1.1 Hamiltonian dieomorphisms 2 1.2 Coisotropic submanifolds 3 1.3 Examples of contact coisotropic submanifolds 9 2 Statement of the results 14 2.1 Assumptions on manifolds 15 2.2 Main theorem 17 2.3 Leafwise coisotropic intersections 18 2.4 Leafwise displacement energy 22 2.5 Rabinowitz Floer homology 23 2.6 Kรผnneth formula 25 2.7 List of related results 27 3 The Rabinowitz action functional with several Lagrange multipliers 28 3.1 The Rabinowitz action functional for coisotropic submanifolds 28 3.2 The perturbed Rabinowitz action functional 30 3.2.1 Compactness 34 3.3 Proof of Theorem A 42 4 The existence of a periodic orbit and the leafwise displacement energy 49 4.1 Proof of Theorem D 50 5 Rabinowitz Floer homology 53 5.1 Boundary Operator 54 5.2 Continuation Homomorphism 58 5.3 Proof of Theorem E 60 5.4 Filtered Rabinowitz Floer Homology 61 5.5 Proof of Theorem B 62 5.6 Proof of Theorem C 65 6 Kรผnneth formula in Rabinowitz Floer homology 69 6.1 Rabinowitz action functional for product manifolds 69 6.1.1 Compactness 71 6.2 Proof of Theorem F 74 6.3 Proof of Theorem G 78 7 Infinitely many leafwise intersection points 83 7.1 Proofs of Corollary F and Corollary G 83 Abstract (in Korean) 95 Acknowledgement (in Korean) 97Docto

    ์กฐ์ง๊ณต์ •์„ฑ ์ธ์‹๊ณผ ์—ญํ• ํŠน์„ฑ์ด ์กฐ์ง๋ชฐ์ž…์— ๋ฏธ์น˜๋Š” ์˜ํ–ฅ ์—ฐ๊ตฌ

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    ํ•™์œ„๋…ผ๋ฌธ (์„์‚ฌ)-- ์„œ์šธ๋Œ€ํ•™๊ต ํ–‰์ •๋Œ€ํ•™์› : ๊ณต๊ธฐ์—…์ •์ฑ…ํ•™๊ณผ, 2015. 8. ์ตœํƒœํ˜„.IMF ์™ธํ™˜์œ„๊ธฐ๋Š” ์šฐ๋ฆฌ์‚ฌํšŒ์— ๋งŽ์€ ์˜ํ–ฅ์„ ๋ฏธ์ณค์ง€๋งŒ ๊ณ ์šฉ์‹œ์žฅ์—์„œ์˜ ๊ฐ€์žฅ ํฐ ๋ณ€ํ™”๋Š” ๋น„์ •๊ทœ์ง์˜ ๋ณธ๊ฒฉ์ ์ธ ๋“ฑ์žฅ์ด์—ˆ๋‹ค. ์ด๋Ÿฌํ•œ ๋น„์ •๊ทœ์ง์˜ ํ™•๋Œ€๋Š” ๊ณ ์šฉ๋ถˆ์•ˆ์˜ ์ฆ๋Œ€, ์ž„๊ธˆ ๋ฐ ๋ณต์ง€ํ›„์ƒ ๋“ฑ ๊ทผ๋กœ์กฐ๊ฑด์—์„œ ์ฐจ๋ณ„ ๋“ฑ ์ •๊ทœ์ง๊ณผ ๋น„๊ตํ•ด ์ƒ๋Œ€์ ์œผ๋กœ ๋ถˆ์ด์ต์„ ๋‹นํ•˜๋Š” ๊ฒฝ์šฐ๊ฐ€ ๋งŽ์•„์ง€๊ฒŒ ๋˜์—ˆ๊ณ  ์ด์— ๋Œ€ํ•œ ๋Œ€์ฑ…์œผ๋กœ ์ •๋ถ€๋Š” 2007๋…„๋ถ€ํ„ฐ ๋น„์ •๊ทœ์ง์„ ์ •๊ทœ์งํ™”ํ•˜๋Š” ์ •์ฑ…์„ ์ถ”์ง„ํ•˜๊ฒŒ ๋˜์—ˆ๋‹ค. ์ด ๊ณผ์ •์—์„œ ์ƒˆ๋กœ์šด ๊ณ ์šฉํ˜•ํƒœ์ธ ๋ฌด๊ธฐ๊ณ„์•ฝ์ง์ด๋ผ๋Š” ๊ฐœ๋… ๋“ฑ์žฅํ•˜๊ธฐ ์‹œ์ž‘ํ•˜์˜€๋Š”๋ฐ ์ด๋“ค์€ ๊ธฐ๊ฐ„์„ ์ •ํ•˜์ง€ ์•Š์€ ๊ทผ๋กœ๊ณ„์•ฝ์„ ์ฒด๊ฒฐํ•œ๋‹ค๋Š” ์ ์—์„œ๋Š” ์ •๊ทœ์ง๊ณผ ์œ ์‚ฌํ•ด ๋ณด์ด์ง€๋งŒ ์ •๊ทœ์ง ๋…ธ๋™์ž์— ๋น„ํ•˜์—ฌ ์ฐจ๋ณ„์  ๊ทผ๋กœ์กฐ๊ฑด์ด ์œ ์ง€๋˜๋Š” ๋…ธ๋™์ž๋กœ ์ •๊ทœ์ง๊ณผ ๋น„์ •๊ทœ์ง์˜ ์ค‘๊ฐ„์ธต์— ์žˆ๋Š” ๋…ธ๋™์ž์ธ ์ค‘๊ทœ์ง์œผ๋กœ ๋ฐ›์•„๋“ค์—ฌ์ง€๊ณ  ์žˆ๋‹ค. ์ด๋Ÿฌํ•œ ์ƒํ™ฉ์†์—์„œ ๊ณต๊ณต๋ถ€๋ฌธ์—์„œ 2007๋…„ ์ดํ›„ ๋ฌด๊ธฐ๊ณ„์•ฝ์ง์€ ๋น ๋ฅด๊ฒŒ ์ฆ๊ฐ€ํ•˜๊ณ  ์žˆ์ง€๋งŒ ์ด์— ๋Œ€ํ•œ ์—ฐ๊ตฌ๋Š” ๋ถ€์กฑํ•œ ์‹ค์ •์ด๋‹ค. ๋ณธ ์—ฐ๊ตฌ๋Š” K๊ณต๊ธฐ์—…์˜ ์ •๊ทœ์ง๊ณผ ๋ฌด๊ธฐ๊ณ„์•ฝ์ง 291๋ช…์„ ๋Œ€์ƒ์œผ๋กœ ์„ค๋ฌธ์กฐ์‚ฌ๋ฅผ ์‹ค์‹œํ•˜๊ณ  ์กฐ์ง๊ณต์ •์„ฑ๊ณผ ์—ญํ• ํŠน์„ฑ์ด ์กฐ์ง๋ชฐ์ž…์— ๋ฏธ์น˜๋Š” ์˜ํ–ฅ์„ ์‹ค์ฆ ๋ถ„์„ํ•˜๊ณ ์ž ํ•˜์˜€๋‹ค. ๋˜ํ•œ ์กฐ์ง๊ณต์ •์„ฑ๊ณผ ์—ญํ• ํŠน์„ฑ์ด ์กฐ์ง๋ชฐ์ž…์˜ ์˜ํ–ฅํšจ๊ณผ์— ์žˆ์–ด ๊ณ ์šฉํŠน์„ฑ(์ •๊ทœ์ง, ๋ฌด๊ธฐ๊ณ„์•ฝ์ง)์ด ์กฐ์ ˆํšจ๊ณผ๊ฐ€ ์žˆ๋Š”์ง€ ๊ฒ€์ฆ์„ ์‹œ๋„ํ•˜์˜€๋‹ค. ์ธก์ •๋ณ€์ˆ˜๋“ค์˜ ํƒ€๋‹น์„ฑ ๋ถ„์„์„ ์œ„ํ•ด ์š”์ธ๋ถ„์„์„ ์‹ค์‹œํ•œ ๊ฒฐ๊ณผ ์กฐ์ง๊ณต์ •์„ฑ์€ ๋ถ„๋ฐฐ๊ณต์ •์„ฑ, ์ ˆ์ฐจ๊ณต์ •์„ฑ, ์ƒํ˜ธ์ž‘์šฉ๊ณต์ •์„ฑ ์„ธ๊ฐ€์ง€ ์š”์ธ์œผ๋กœ ๋ถ„๋ฅ˜๋˜์—ˆ์œผ๋ฉฐ, ์—ญํ• ํŠน์„ฑ๋„ ๋งˆ์ฐฌ๊ฐ€์ง€๋กœ ์—ญํ• ๊ฐˆ๋“ฑ, ์—ญํ• ๋ชจํ˜ธ์„ฑ, ์—ญํ• ๊ณผ์ค‘์œผ๋กœ ๋ถ„๋ฅ˜๋˜์—ˆ๊ณ  ์กฐ์ง๋ชฐ์ž…๋„ ์ •์„œ์ ๋ชฐ์ž…, ์ง€์†์ ๋ชฐ์ž…, ๊ทœ๋ฒ”์ ๋ชฐ์ž…์œผ๋กœ ๋ถ„๋ฅ˜๋˜์–ด ๊ธฐ์กด ์„ ํ–‰์—ฐ๊ตฌ์˜ ๊ฒฐ๊ณผ์™€ ๊ฐ™์ด ๋ถ„์„๋˜์—ˆ๋‹ค. ๋˜ํ•œ ์ธก์ •๋ณ€์ˆ˜์˜ ์‹ ๋ขฐ์„ฑ ๋ถ„์„์„ ์œ„ํ•ด ํฌ๋ก ๋ฐ”ํ•˜ ์•ŒํŒŒ๊ฐ’ ๋ถ„์„๊ฒฐ๊ณผ ์‚ฌํšŒ๊ณผํ•™์—์„œ ์ผ๋ฐ˜์ ์œผ๋กœ ๋ฐ›์•„๋“ค์—ฌ์ง€๋Š” 0.6์ด์ƒ์œผ๋กœ ์ธก์ •๋˜์–ด ๋‚ด์ ์ผ๊ด€์„ฑ๋„ ํ™•๋ณด๋˜์—ˆ๋‹ค. ๊ฐ ๋ณ€์ˆ˜๋“ค๊ฐ„์— ์ƒ๊ด€๊ด€๊ณ„ ๋ถ„์„๊ฒฐ๊ณผ ํ†ต๊ณ„์ ์œผ๋กœ ์œ ์˜๋ฏธํ•œ ๊ฒƒ์œผ๋กœ ๋‚˜ํƒ€๋‚˜์„œ ์กฐ์ง๊ณต์ •์„ฑ๊ณผ ์—ญํ• ํŠน์„ฑ์ด ์กฐ์ง๋ชฐ์ž…์— ๊ฐœ๋žต์ ์œผ๋กœ ์—ฐ๊ด€์„ฑ์ด ์žˆ์Œ์„ ์•Œ ์ˆ˜ ์žˆ์—ˆ์œผ๋ฉฐ ๋…๋ฆฝ๋ณ€์ˆ˜๊ฐ„ ์ƒ๊ด€๊ด€๊ณ„๊ฐ€ 0.8 ์ด์ƒ์ธ ๋ณ€์ˆ˜๋“ค์ด ๋‚˜ํƒ€๋‚˜์ง€ ์•Š์•„์„œ ๋‹ค์ค‘๊ณต์„ ์„ฑ์˜ ๋ฌธ์ œ๋„ ๋ฐœ์ƒํ•  ๊ฐ€๋Šฅ์„ฑ์ด ๋‚ฎ๊ฒŒ ๋ถ„์„๋˜์—ˆ๋‹ค. ์กฐ์ง๊ณต์ •์„ฑ(๋ถ„๋ฐฐ๊ณต์ •์„ฑ, ์ ˆ์ฐจ๊ณต์ •์„ฑ, ์ƒํ˜ธ์ž‘์šฉ๊ณต์ •์„ฑ)๊ณผ ์—ญํ• ํŠน์„ฑ(์—ญํ• ๊ฐˆ๋“ฑ, ์—ญํ• ๋ชจํ˜ธ์„ฑ, ์—ญํ• ๊ณผ์ค‘)์ด ์กฐ์ง๋ชฐ์ž…์— ์–ด๋– ํ•œ ์˜ํ–ฅ์„ ๋ฏธ์น˜๋Š”์ง€ ๋ถ„์„ํ•˜๊ธฐ ์œ„ํ•ด ํšŒ๊ท€๋ถ„์„์„ ์‹ค์‹œํ•˜์˜€๋‹ค. ๋‹จ, ์กฐ์ง๋ชฐ์ž…์„ ๊ฒ€์ฆํ•จ์— ์žˆ์–ด์„œ ์กฐ์ง์— ๋Œ€ํ•œ ์ „๋ฐ˜์ ์ธ ์ˆ˜์ค€์„ ๋ฐ˜์˜ํ•˜๊ธฐ ์œ„ํ•ด ์ •์„œ์  ๋ชฐ์ž…, ์ง€์†์  ๋ชฐ์ž…, ๊ทœ๋ฒ”์  ๋ชฐ์ž…์„ ํ†ตํ•ฉํ•˜์—ฌ ๋ถ„์„์— ํ™œ์šฉํ•˜์˜€๋‹ค. ๋จผ์ € ํ†ต์ œ๋ณ€์ˆ˜ ์ค‘์—์„œ๋Š” ์—ฐ๋ น๋ณ€์ˆ˜๋งŒ์ด ์กฐ์ง๋ชฐ์ž…์— ์œ ์˜ํ•œ ์˜ํ–ฅ์ด ์žˆ์—ˆ์œผ๋ฉฐ ์กฐ์ง๊ณต์ •์„ฑ๋ณ€์ˆ˜์˜ ํ•˜์œ„๋ณ€์ˆ˜ ์ค‘์—์„œ๋Š” ๋ถ„๋ฐฐ๊ณต์ •์„ฑ ๋ณ€์ˆ˜์™€ ์ƒํ˜ธ์ž‘์šฉ๊ณต์ •์„ฑ์ด ์กฐ์ง๋ชฐ์ž…์— ์ •(+)์˜ ๋ฐฉํ–ฅ์œผ๋กœ ์œ ์˜ํ•œ ์˜ํ–ฅ์ด ์žˆ๋Š” ๊ฒƒ์œผ๋กœ ๋ถ„์„๋˜์—ˆ๋Š”๋ฐ ์ด๋Š” ๊ธฐ์กด์˜ ์„ ํ–‰์—ฐ๊ตฌ์—์„œ์™€ ๊ฐ™์ด ์กฐ์ง๊ณต์ •์„ฑ๊ณผ ์กฐ์ง๋ชฐ์ž…์ด ์ •(+)์˜ ๊ด€๊ณ„์— ์žˆ์Œ์„ ์‹ค์ฆํ•œ ๊ฒƒ์ด๋‹ค. ๋˜ํ•œ, ์—ญํ• ํŠน์„ฑ๋ณ€์ˆ˜๋Š” ์—ญํ• ๋ชจํ˜ธ์„ฑ ๋ณ€์ˆ˜๋งŒ์ด ์กฐ์ง๋ชฐ์ž…์— ๋ถ€(-)์˜ ๋ฐฉํ–ฅ์œผ๋กœ ์œ ์˜ํ•œ ์˜ํ–ฅ์ด ์žˆ์—ˆ๋Š”๋ฐ ์ด ๋˜ํ•œ ๋Œ€์ฒด์ ์ธ ์„ ํ–‰์—ฐ๊ตฌ์™€ ๊ฐ™์€ ๊ฒฐ๊ณผ์ด๋‹ค. ์กฐ์ง๊ณต์ •์„ฑ๊ณผ ์—ญํ• ํŠน์„ฑ์ด ์กฐ์ง๋ชฐ์ž…์˜ ์˜ํ–ฅํšจ๊ณผ์— ์žˆ์–ด ๊ณ ์šฉํ˜•ํƒœ์˜ ์กฐ์ ˆํšจ๊ณผ๋ฅผ ๊ฒ€์ฆํ•˜๊ธฐ ์œ„ํ•˜์—ฌ ๊ณ ์šฉํ˜•ํƒœ๋ฅผ ์ •๊ทœ์ง๊ณผ ๋ฌด๊ธฐ๊ณ„์•ฝ์ง์œผ๋กœ ๊ตฌ๋ถ„ํ•˜์—ฌ ๋”๋ฏธ๋ณ€์ˆ˜๋กœ ์ฒ˜๋ฆฌํ•˜๊ณ  ์ƒํ˜ธ์ž‘์šฉํ•ญ์„ ๋งŒ๋“ค์–ด ์‚ฝ์ž…ํ•œ ๋‹ค์Œ ๋‹ค์ค‘ํšŒ๊ท€ ๋ถ„์„์„ ์‹ค์‹œํ•œ ๊ฒฐ๊ณผ ๊ณ ์šฉํ˜•ํƒœ์— ์˜ํ•œ ์กฐ์ ˆํšจ๊ณผ๊ฐ€ ์—†๋Š” ๊ฒƒ์œผ๋กœ ๋ถ„์„๋˜์—ˆ๋‹ค. ์กฐ์ง๋ชฐ์ž…์— ๋ถ„๋ฐฐ๊ณต์ •์„ฑ, ์ƒํ˜ธ์ž‘์šฉ๊ณต์ •์„ฑ ๊ทธ๋ฆฌ๊ณ  ์—ญํ• ๋ชจํ˜ธ์„ฑ์ด ์ค‘์š”ํ•œ ์˜ํ–ฅ์„ ๋ฏธ์น˜๊ณ  ์žˆ์—ˆ์œผ๋ฉฐ ๊ณ ์šฉํ˜•ํƒœ๋Š” ์กฐ์ ˆํšจ๊ณผ๊ฐ€ ์—†๋Š” ๊ฒƒ์œผ๋กœ ๋‚˜ํƒ€๋‚œ ๊ฒฐ๊ณผ๋ฅผ K๊ณต๊ธฐ์—…์˜ ์ œ๋„์  ๋ณ€์ฒœ ๊ณผ์ •, ์กฐ์ง์  ํŠน์„ฑ ๋ฐ ์—ฌ๊ฑด, ๋ฌธํ™”์  ์ธก๋ฉด์„ ์ข…ํ•ฉ์ ์œผ๋กœ ๊ณ ๋ คํ•˜์—ฌ ํŒ๋‹จํ•œ ๊ฒฐ๊ณผ ๋ถ„๋ฐฐ๊ณต์ •์„ฑ์˜ ๋ฌธ์ œ๊ฐ€ ํฌ๊ฒŒ ๋‚˜ํƒ€๋‚œ ๊ฒƒ์€ K๊ณต๊ธฐ์—…์ด ์—ฐ๋ด‰์ œ์˜ ์กฐ๊ธฐ๋„์ž…์œผ๋กœ ์ธํ•œ ์„ฑ๊ณผ๊ธ‰์˜ ์ฐจ์ด, ๊ทธ๋ฃน์‚ฌ ๋‚ด์—์„œ ์ƒ๋Œ€์ ์œผ๋กœ ์ ์€ ์ง์›ํ‰๊ท ๋ณด์ˆ˜์—์„œ ๊ทธ ์›์ธ์„ ์ฐพ์„ ์ˆ˜ ์žˆ์œผ๋ฉฐ, ์ƒํ˜ธ์ž‘์šฉ๊ณต์ •์„ฑ์˜ ๋ฌธ์ œ๊ฐ€ ๋Œ€๋‘๋œ ๊ฒƒ์€ K๊ณต๊ธฐ์—…์˜ ์ง์›๋“ค์€ ์ƒ์‚ฌ์˜ ์—…๋ฌด์ง€์‹œ๊ฐ€ ์ „๋‹ฌ๋˜๋Š” ๋ฐฉ์‹์— ์˜๋ฏธ๋ฅผ ๋‘๊ณ  ์žˆ์œผ๋ฉฐ ์œ„๊ณ„์ ์ด๊ณ  ๊ถŒ์œ„์ ์ธ ์กฐ์ง๋ฌธํ™”๋กœ ์ธํ•ด ๋ฏผ๊ฐ๋„๊ฐ€ ๋†’์•„ ์กŒ์„ ๊ฒƒ์œผ๋กœ ๋ถ„์„๋˜์—ˆ๋‹ค. ๋˜ํ•œ ์ •๊ทœ์ง๊ณผ ๋ฌด๊ธฐ๊ณ„์•ฝ์ง๊ฐ„์— ๋ถ„๋ฐฐ๊ณต์ •์„ฑ๊ณผ ์ƒํ˜ธ์ž‘์šฉ๊ณต์ •์„ฑ์ด ์กฐ์ง๋ชฐ์ž…์— ๋ฏธ์น˜๋Š” ์˜ํ–ฅ์— ์žˆ์–ด ๊ณ ์šฉํ˜•ํƒœ์˜ ์ฐจ์ด๊ฐ€ ์œ ์˜๋ฏธํ•œ ์˜ํ–ฅ์ด ์—†๋Š” ๊ฒƒ์œผ๋กœ ๋‚˜ํƒ€๋‚œ ๊ฒƒ์€ ๋ฌด๊ธฐ๊ณ„์•ฝ์ง์˜ ๊ธ‰์—ฌ๊ฐ€ ์ •๊ทœ์ง์˜ 90%์ˆ˜์ค€์œผ๋กœ ํ–ฅ์ƒ๋œ ๊ฒƒ, ์ •๊ทœ์ง๊ณผ ๋™์ผํ•œ ์ •๋…„์—ฐ์žฅ, ๋ฌด๊ธฐ๊ณ„์•ฝ์ง์˜ ์ •๊ทœ์ง ๋…ธ๋™์กฐํ•ฉ ๊ฐ€์ž… ๋“ฑ๊ณผ ๊ฐ™์€ ์šฐํ˜ธ์ ์ธ ์ œ๋„์˜ ์‹ค์‹œ๋กœ ์ธํ•ด ์ •๊ทœ์ง๊ณผ ๋ฌด๊ธฐ๊ณ„์•ฝ์ง๊ฐ„์— ๊ฐ„๊ทน์„ ์ขํžˆ๊ณ  ๋™์งˆ๊ฐ์„ ๋†’์˜€์„ ๊ฒƒ์œผ๋กœ ํŒŒ์•…ํ•  ์ˆ˜ ์žˆ์—ˆ๋‹ค. ๋˜ํ•œ ์—ญํ• ๋ชจํ˜ธ์„ฑ์˜ ๋ฌธ์ œ๋Š” ๊ณต์ ์ธ ๊ธฐ๋Šฅ ์ˆ˜ํ–‰๊ณผ ๋”๋ถˆ์–ด ์ˆ˜์ต์ถ”๊ตฌ์˜ ์—ญํ• ์ด ๋™์‹œ์— ์ถ”๊ตฌ๋˜๋Š” ๊ฒƒ๊ณผ ๊ฐ™์ด ๊ณผ์—…์ž์ฒด๊ฐ€ ๋ณต์žกํ•˜๊ณ  ๋‹ค์–‘ํ•œ ๊ฐ€์น˜๊ฐ€ ๋™์‹œ์— ์š”๊ตฌ๋จ์œผ๋กœ ์ธํ•ด ์ฆํญ๋˜์—ˆ์„ ๊ฒƒ์œผ๋กœ ํŒŒ์•…ํ•  ์ˆ˜ ์žˆ์—ˆ์œผ๋ฉฐ ์—ญํ• ๋ชจํ˜ธ์„ฑ์ด ์กฐ์ง๋ชฐ์ž…์˜ ์˜ํ–ฅํšจ๊ณผ์— ์žˆ์–ด ์œ ์˜๋ฏธํ•œ ๊ฒฐ๊ณผ๊ฐ€ ๋‚˜ํƒ€๋‚˜์ง€ ์•Š์€ ๊ฒƒ์€ ์ •๊ทœ์ง๊ณผ ๋ฌด๊ธฐ๊ณ„์•ฝ์ง์ด ๋™์ผํ•œ ๊ฒฝํ—˜์„ ํ•˜๊ณ  ์žˆ๋Š” ๊ฒƒ์œผ๋กœ ๋ณผ ์ˆ˜ ์žˆ๋‹ค. ๊ฒฐ๋ก ์ ์œผ๋กœ ์ž„๊ธˆ ๋ฐ ์„ฑ๊ณผ๊ธ‰๊ณผ ๊ฐ™์€ ๋ถ„๋ฐฐ๊ณต์ •์„ฑ์˜ ๋ฌธ์ œ๋Š” ์ •๋ถ€์˜ ํ†ต์ œ๋ฅผ ๋ฐ›๊ธฐ ๋•Œ๋ฌธ์— ์ฆ‰๊ฐ์ ์ธ ๊ฐœ์„ ์ด ์–ด๋ ต๋‹ค ํ•˜๋”๋ผ๋„ ์ƒํ˜ธ์ž‘์šฉ๊ณต์ •์„ฑ์˜ ๋ฌธ์ œ๋Š” ์—…๋ฌด์ง€์‹œ๋‚˜ ๋ช…๋ น์„ ์ „๋‹ฌํ•˜๋Š” ๋ฌธ์ œ์— ์žˆ์–ด์„œ ๋ฐœ์ƒํ•˜๋Š” ๋ฌธ์ œ์ด๋ฏ€๋กœ ๋ณด์ง์ž๋“ค์„ ์ค‘์‹ฌ์œผ๋กœ ์กฐ์ง ๋ถ„์œ„๊ธฐ๋ฅผ ์‡„์‹ ํ•˜๋ ค๋Š” ๋…ธ๋ ฅ์ด ํ•„์š”ํ•˜๋ฉฐ, ์—ญํ• ๋ชจํ˜ธ์„ฑ์˜ ๋ฌธ์ œ๋Š” ์ •ํ™•ํ•œ ์ง๋ฌด๋ถ„์„์„ ํ†ตํ•ด ์—…๋ฌด๋ฅผ ๋ช…ํ™•ํžˆ ๊ทœ์ •ํ•˜๋ ค๋Š” ๋…ธ๋ ฅ์ด ๊ธฐ์šธ์—ฌ์ ธ์•ผ ํ•  ๊ฒƒ์ด๋‹ค. ์ฃผ์š”์–ด : ๋ฌด๊ธฐ๊ณ„์•ฝ์ง, ์กฐ์ง๊ณต์ •์„ฑ, ์—ญํ• ํŠน์„ฑ, ์กฐ์ง๋ชฐ์ž… ํ•™ ๋ฒˆ : 2014-23593๋ชฉ ์ฐจ ์ œ 1 ์žฅ ์„œ ๋ก  1 ์ œ 1 ์ ˆ ์—ฐ๊ตฌ์˜ ํ•„์š”์„ฑ ๋ฐ ๋ชฉ์  1 ์ œ 2 ์ ˆ ์—ฐ๊ตฌ์˜ ๋Œ€์ƒ ๋ฐ ๋ฐฉ๋ฒ• 6 ์ œ 2 ์žฅ ์ด๋ก ์  ๋ฐฐ๊ฒฝ ๋ฐ ์„ ํ–‰์—ฐ๊ตฌ ๊ฒ€ํ†  7 ์ œ 1 ์ ˆ ๋ฌด๊ธฐ๊ณ„์•ฝ์ง์— ๋Œ€ํ•œ ์ด๋ก ์  ๋…ผ์˜ 7 1. ๋ฌด๊ธฐ๊ณ„์•ฝ์ง์˜ ๊ฐœ๋… ๋ฐ ์„ฑ๊ฒฉ 7 ๊ฐ€. ๋ฌด๊ธฐ๊ณ„์•ฝ์ง์˜ ๊ฐœ๋… 7 ๋‚˜. ๋ฌด๊ธฐ๊ณ„์•ฝ์ง์˜ ์„ฑ๊ฒฉ 8 2. ๋ฌด๊ธฐ๊ณ„์•ฝ์ง ์ „ํ™˜ ํ›„ ์Ÿ์  10 ๊ฐ€. ๋ฏธํกํ•œ ๋ณด์ƒ ์ˆ˜์ค€์˜ ๋ฌธ์ œ 10 ๋‚˜. ์ •๊ทœ์ง๊ณผ ์œ ์‚ฌ ์—…๋ฌด ์ˆ˜ํ–‰ ๋ฐ ๊ถŒํ•œ ์ œํ•œ์˜ ๋ฌธ์ œ 11 ์ œ 2 ์ ˆ ์กฐ์ง๊ณต์ •์„ฑ 12 1. ์กฐ์ง๊ณต์ •์„ฑ์˜ ์ด๋ก ์  ์ฒด๊ณ„ ๋…ผ์˜ 12 2. ์กฐ์ง๊ณต์ •์„ฑ์˜ ์œ ํ˜• 14 ๊ฐ€. ๋ถ„๋ฐฐ๊ณต์ •์„ฑ 14 ๋‚˜. ์ ˆ์ฐจ๊ณต์ •์„ฑ 15 ๋‹ค. ์ƒํ˜ธ์ž‘์šฉ๊ณต์ •์„ฑ 16 ์ œ 3 ์ ˆ ์—ญํ• ํŠน์„ฑ 17 1. ์—ญํ• ํŠน์„ฑ์˜ ์ด๋ก ์  ์ฒด๊ณ„ ๋…ผ์˜ 17 2. ์—ญํ• ํŠน์„ฑ์˜ ์œ ํ˜• 18 ๊ฐ€. ์—ญํ• ๊ฐˆ๋“ฑ(role conflict) 18 ๋‚˜. ์—ญํ• ๋ชจํ˜ธ์„ฑ(role ambiguity) 18 ๋‹ค. ์—ญํ• ๊ณผ์ค‘(role overload) 19 ์ œ 4 ์ ˆ ์กฐ์ง๋ชฐ์ž… 20 1. ์กฐ์ง๋ชฐ์ž…์˜ ์ด๋ก ์  ์ฒด๊ณ„ ๋…ผ์˜ 20 2. ์กฐ์ง๋ชฐ์ž…์˜ ์œ ํ˜• 22 ๊ฐ€. ์ •์„œ์  ๋ชฐ์ž…(affective commitment) 22 ๋‚˜. ์ง€์†์  ๋ชฐ์ž…(continuous commitment) 23 ๋‹ค. ๊ทœ๋ฒ”์  ๋ชฐ์ž…(normative commitment) 23 ์ œ 5 ์ ˆ ์„ ํ–‰์—ฐ๊ตฌ ๊ฒ€ํ†  24 1. ์กฐ์ง๊ณต์ •์„ฑ๊ณผ ์กฐ์ง๋ชฐ์ž…์˜ ๊ด€๊ณ„์— ๋Œ€ํ•œ ์„ ํ–‰์—ฐ๊ตฌ ๊ฒ€ํ†  24 ๊ฐ€. ์กฐ์ง๊ณต์ •์„ฑ๊ณผ ์กฐ์ง๋ชฐ์ž…์— ๋Œ€ํ•œ ์„ ํ–‰์—ฐ๊ตฌ 24 ๋‚˜. ๊ณ ์šฉํ˜•ํƒœ์— ๋”ฐ๋ฅธ ๊ณต์ •์„ฑ๊ณผ ์กฐ์ง๋ชฐ์ž…์— ๊ด€ํ•œ ์„ ํ–‰์—ฐ๊ตฌ 25 2. ์—ญํ• ํŠน์„ฑ๊ณผ ์กฐ์ง๋ชฐ์ž…์— ๋Œ€ํ•œ ์„ ํ–‰์—ฐ๊ตฌ ๊ฒ€ํ†  27 ๊ฐ€. ์—ญํ• ํŠน์„ฑ๊ณผ ์กฐ์ง๋ชฐ์ž…์— ๋Œ€ํ•œ ์„ ํ–‰์—ฐ๊ตฌ 27 ๋‚˜. ๊ณ ์šฉํ˜•ํƒœ์— ๋”ฐ๋ฅธ ์—ญํ• ํŠน์„ฑ๊ณผ ์กฐ์ง๋ชฐ์ž…์— ๊ด€ํ•œ ์„ ํ–‰์—ฐ๊ตฌ 28 3. ์กฐ์ง๋ชฐ์ž…์— ๋Œ€ํ•œ ์„ ํ–‰์—ฐ๊ตฌ ๊ฒ€ํ†  28 ๊ฐ€. ๋ฌด๊ธฐ๊ณ„์•ฝ์ง์˜ ์กฐ์ง๋ชฐ์ž…์— ๋Œ€ํ•œ ์—ฐ๊ตฌ 28 ๋‚˜. ๋น„์ •๊ทœ์ง์˜ ์กฐ์ง๋ชฐ์ž…์— ๋Œ€ํ•œ ์—ฐ๊ตฌ 30 ๋‹ค. ์กฐ์ง๋ชฐ์ž…์— ๋Œ€ํ•œ ์„ ํ–‰๋ณ€์ˆ˜์— ๋Œ€ํ•œ ์—ฐ๊ตฌ 31 ์ œ 3 ์žฅ ์—ฐ๊ตฌ์„ค๊ณ„ 33 ์ œ 1 ์ ˆ ์—ฐ๊ตฌ๋ชจํ˜• ๋ฐ ๊ฐ€์„ค์˜ ์„ค์ • 33 1. ์—ฐ๊ตฌ๋ชจํ˜• 33 2. ์—ฐ๊ตฌ๊ฐ€์„ค์˜ ์„ค์ • 34 ์ œ 2 ์ ˆ ๋ณ€์ˆ˜์˜ ์กฐ์ž‘์  ์ •์˜์™€ ์ธก์ • 35 1. ๋…๋ฆฝ๋ณ€์ˆ˜์˜ ์„ ์ • ๋ฐ ์ธก์ • : ์กฐ์ง๊ณต์ •์„ฑ, ์—ญํ• ํŠน์„ฑ 35 ๊ฐ€. ์กฐ์ง๊ณต์ •์„ฑ 35 ๋‚˜. ์—ญํ• ํŠน์„ฑ 36 2. ์ข…์†๋ณ€์ˆ˜์˜ ์„ ์ • ๋ฐ ์ธก์ • : ์กฐ์ง๋ชฐ์ž… 36 3. ํ†ต์ œ๋ณ€์ˆ˜ ๋ฐ ์กฐ์ ˆ๋ณ€์ˆ˜ 36 ์ œ 3 ์ ˆ ์ž๋ฃŒ์ˆ˜์ง‘ ๋ฐ ๋ถ„์„๋ฐฉ๋ฒ• 37 1. ์ž๋ฃŒ์˜ ์ˆ˜์ง‘ 37 2. ๋ถ„์„๋ฐฉ๋ฒ• 38 ์ œ 4 ์žฅ ์‹ค์ฆ๋ถ„์„ 39 ์ œ 1 ์ ˆ ํ‘œ๋ณธ์˜ ํŠน์„ฑ 39 ์ œ 2 ์ ˆ ์ธก์ •๋„๊ตฌ์˜ ํƒ€๋‹น์„ฑ ๋ฐ ์‹ ๋ขฐ์„ฑ ๊ฒ€์ฆ 41 1. ํƒ€๋‹น์„ฑ ๊ฒ€์ฆ 41 2. ์‹ ๋ขฐ์„ฑ ๊ฒ€์ฆ 47 ์ œ 3 ์ ˆ ๋ณ€์ˆ˜๊ฐ„ ์ƒ๊ด€๊ด€๊ณ„ ๋ถ„์„ 51 ์ œ 4 ์ ˆ ๊ฐ€์„ค์˜ ๊ฒ€์ฆ 54 1. ์กฐ์ง๊ณต์ •์„ฑ ์ธ์‹๊ณผ ์กฐ์ง๋ชฐ์ž…๊ณผ์˜ ๊ด€๊ณ„ 54 2. ์—ญํ• ํŠน์„ฑ๊ณผ ์กฐ์ง๋ชฐ์ž…๊ณผ์˜ ๊ด€๊ณ„ 58 3. ์กฐ์ง๊ณต์ •์„ฑ๊ณผ ์กฐ์ง๋ชฐ์ž… ์กฐ์ ˆํšจ๊ณผ ๋ถ„์„ 62 4. ์—ญํ• ํŠน์„ฑ๊ณผ ์กฐ์ง๋ชฐ์ž… ์กฐ์ ˆํšจ๊ณผ ๋ถ„์„ 65 ์ œ 5 ์ ˆ ์ข…ํ•ฉ์  ํ† ์˜ 68 1. ์‹ค์ฆ์  ์—ฐ๊ตฌ ๊ฒฐ๊ณผ ์š”์•ฝ 68 2. ์ข…ํ•ฉ์  ํ† ์˜ 72 ๊ฐ€. ๋ฌด๊ธฐ๊ณ„์•ฝ์ง์— ๋Œ€ํ•œ ์ฒ˜์šฐ ๊ฐœ์„  73 ๋‚˜. ์—ฐ๋ด‰์ œ์˜ ์กฐ๊ธฐ๋„์ž… ๋ฐ ์ƒ๋Œ€์ ์œผ๋กœ ์ ์€ ์ง์› ํ‰๊ท  ๋ณด์ˆ˜ 74 ๋‹ค. ๊ณต๊ธฐ์—…์œผ๋กœ์„œ ์œ„๊ณ„์  ์กฐ์ง๋ฌธํ™” 75 ๋ผ. ๊ณต์ ๊ธฐ๋Šฅ๊ณผ ์‚ฌ์ ๊ธฐ๋Šฅ์˜ ๋™์‹œ ์ˆ˜ํ–‰์œผ๋กœ ์ธํ•œ ๋‹ค์–‘ํ•œ ๊ฐ€์น˜ ์ถ”๊ตฌ 75 ์ œ 5 ์žฅ ๊ฒฐ ๋ก  76 ์ œ 1 ์ ˆ ์—ฐ๊ตฌ์˜ ํ•จ์˜ ๋ฐ ์‹œ์‚ฌ์  76 ์ œ 2 ์ ˆ ์—ฐ๊ตฌ์˜ ํ•œ๊ณ„ ๋ฐ ํ›„์†์—ฐ๊ตฌ ์ œ์•ˆ 78 ์ฐธ๊ณ ๋ฌธํ—Œ 80 ์„ค๋ฌธ์ง€ 87 Abstract 92Maste

    Digging Gangnam Style : Transmedia Storytelling in K-pop

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    ์ด ๋…ผ๋ฌธ์€ ์ผ€์ดํŒ(K-pop)์—์„œ์˜ ํŠธ๋žœ์Šค๋ฏธ๋””์–ด(transmedia) ์Šคํ† ๋ฆฌํ…”๋ง ํ˜„์ƒ๊ณผ ์ „๋žต์— ๋Œ€ํ•œ ์—ฐ๊ตฌ๋‹ค. ์ด ๋…ผ๋ฌธ์€ ์ตœ๊ทผ ์œ ํŠœ๋ธŒ๋ฅผ ์ค‘์‹ฌ์œผ๋กœ ์ „ ์„ธ๊ณ„์— ํ™•์‚ฐ๋˜์–ด ์„ ํ’์ ์ธ ์ธ๊ธฐ๋ฅผ ๋Œ๊ณ  ์žˆ๋Š” ์‚ฌ๋ก€๋ฅผ ์ค‘์‹ฌ์œผ๋กœ ์ˆ˜์šฉ์ž๋“ค์— ์˜ํ•ด ์ œ์ž‘๋˜๊ณ  ํ™•์‚ฐ๋œ ๋ฐˆ(meme) ๋น„๋””์˜ค์— ๋Œ€ํ•œ ๋ถ„์„์„ ์ˆ˜ํ–‰ํ•˜๊ณ ์ž ํ•œ๋‹ค. ๋ฐˆ๋น„๋””์˜ค๋Š” ํŠธ๋žœ์Šค๋ฏธ๋””์–ด ์Šคํ† ๋ฆฌํ…”๋ง์— ๋Œ€ํ•œ ์ดํ•ด์—์„œ ์ˆ˜์šฉ์ž์˜ ์ฝ˜ํ…์ธ  ์†Œ๋น„, ์ƒ์‚ฐ๊ณผ ์œ ํ†ต์„ ํฌํ•จํ•œ ๋””์ง€ํ„ธ ์ˆ˜์šฉ์ž๋“ค์˜ ์ฝ˜ํ…์ธ  ์ˆ˜์šฉ๋ฐฉ์‹์— ๋Œ€ํ•œ ์ดํ•ด, ์ฆ‰ ๋””์ง€ํ„ธ ํŒฌ๋ค(digital fandom)์— ๋Œ€ํ•œ ์ดํ•ด์— ์žˆ์–ด ํ•ต์‹ฌ์ ์ด๋‹ค. ์ด ๋…ผ๋ฌธ์€ ์˜จ๋ผ์ธ ๋Œ€์ค‘์Œ์•…์‚ฐ์—…์—์„œ ํŒฌ ์ค‘์‹ฌ์˜ ํŠธ๋žœ์Šค๋ฏธ๋””์–ด ์Šคํ† ๋ฆฌํ…”๋ง์ด๋ž€ ๋ฌด์—‡์ด๋ฉฐ ์–ด๋–ป๊ฒŒ ๊ฐ€๋Šฅํ•œ์ง€์— ๋Œ€ํ•œ ๋…ผ์˜๋ฅผ ์ œ์‹œํ•˜๊ณ  ์•ž์œผ๋กœ ์ผ€์ดํŒ ์‚ฐ์—…์—์„œ ํŠธ๋žœ์Šค๋ฏธ๋””์–ด ์Šคํ† ๋ฆฌํ…”๋ง ์ „๋žต์„ ๊ณ ์ฐฐํ•˜๊ณ  ์ˆ˜๋ฆฝํ•˜๋Š” ๋ฐ ์˜ ์„ฑ๊ณต์ด ์ฃผ๋Š” ํ•จ์˜์— ๋Œ€ํ•˜์—ฌ ๋…ผ์˜ํ•  ๊ฒƒ์ด๋‹ค.This paper examines some issues regarding transmedia storytelling in the context of Kโ€pop(Korean pop). Focusing on the recent success of สนGangnam Styleสน by PSY, a Korean popโ€singer, which has been widely distributed primarily through Youtube, this study will investigate the diffusion and reception process of Gangnam Style music video as Hallyu contents. Particularly, this paper analyzes a variety of Gangnam Styleโ€meme videos, which has been also diffused through Youtube. This paper suggests that meme videos are a significant content as an object of study that is mainly distributed, received and produced by many contemporary popular music fans and thus helps us understand how fanโ€based transmedia storytelling works in online popular music industries. We conclude this study by discussing the implications of the success of Gangnam Style contents including the meme videos in thinking about the meanings and strategies of transmedia storytelling in seemingly expanding popular music (particularly Kโ€pop) industries in Korea.์ด ๋…ผ๋ฌธ์€ 2010๋…„๋„ ์ •๋ถ€์žฌ์›(๊ต์œก๊ณผํ•™๊ธฐ์ˆ ๋ถ€ ์ธ๋ฌธ์‚ฌํšŒ์—ฐ๊ตฌ์—ญ๋Ÿ‰๊ฐ•ํ™”์‚ฌ์—…๋น„)์œผ๋กœ ํ•œ๊ตญ์—ฐ๊ตฌ์žฌ๋‹จ์˜ ์ง€์›์„ ๋ฐ›์•„ ์—ฐ๊ตฌ๋˜์—ˆ์Œ(NRF-2010-330-B00040)
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