메뉴 건너뛰기




Volumn 8, Issue 1, 1997, Pages 77-90

Generalized spectral decomposition and intrinsic irreversibility of the Arnold Cat map

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0002404859     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(96)00056-2     Document Type: Article
Times cited : (16)

References (36)
  • 4
    • 84990727688 scopus 로고
    • Generalized spectral decomposition of mixing dynamical systems
    • I. Antoniou and S. Tasaki, Generalized spectral decomposition of mixing dynamical systems. Int. J. Quant. Chem. 46, 425-474 (1993).
    • (1993) Int. J. Quant. Chem. , vol.46 , pp. 425-474
    • Antoniou, I.1    Tasaki, S.2
  • 5
  • 6
    • 17844380546 scopus 로고
    • Spectral decomposition of the Renyi map
    • I. Antoniou and S. Tasaki, Spectral decomposition of the Renyi map. J. Phys. A 26, 73-94 (1993).
    • (1993) J. Phys. A , vol.26 , pp. 73-94
    • Antoniou, I.1    Tasaki, S.2
  • 7
    • 44049120431 scopus 로고
    • Generalized spectral decomposition of the β-adic Baker's transformation and intrinsic irreversibility
    • I. Antoniou and S. Tasaki, Generalized spectral decomposition of the β-adic Baker's transformation and intrinsic irreversibility. Physica A 190, 303-329 (1992).
    • (1992) Physica A , vol.190 , pp. 303-329
    • Antoniou, I.1    Tasaki, S.2
  • 12
    • 17044374336 scopus 로고
    • On the rate of mixing of Axiom A flow
    • M. Pollicott, On the rate of mixing of Axiom A flow. Invent. Math. 81, 413-426 (1985); Meromorphic extensions of generalized zeta functions. Ibid. 85, 147-164.
    • (1985) Invent. Math. , vol.81 , pp. 413-426
    • Pollicott, M.1
  • 13
    • 33646978879 scopus 로고    scopus 로고
    • Meromorphic extensions of generalized zeta functions
    • M. Pollicott, On the rate of mixing of Axiom A flow. Invent. Math. 81, 413-426 (1985); Meromorphic extensions of generalized zeta functions. Ibid. 85, 147-164.
    • Invent. Math. , vol.85 , pp. 147-164
  • 14
    • 0001337517 scopus 로고
    • Resonances of chaotic dynamical systems
    • D. Ruelle, Resonances of chaotic dynamical systems. Phys. Rev. Lett. 56, 405-407 (1989).
    • (1989) Phys. Rev. Lett. , vol.56 , pp. 405-407
    • Ruelle, D.1
  • 16
    • 51649157555 scopus 로고
    • An extension of the theory of Fredholm determinants
    • D. Ruelle, An extension of the theory of Fredholm determinants, Publ Math. IHES 72, 175-193 (1990).
    • (1990) Publ Math. IHES , vol.72 , pp. 175-193
    • Ruelle, D.1
  • 17
    • 0001741383 scopus 로고
    • Time correlation functions of one dimensional transformations
    • H. Mori, B. So and T. Ose, Time correlation functions of one dimensional transformations. Prog. Theor. Phys. 66, 1266-1283 (1981).
    • (1981) Prog. Theor. Phys. , vol.66 , pp. 1266-1283
    • Mori, H.1    So, B.2    Ose, T.3
  • 18
    • 0002161851 scopus 로고
    • Spectrum and eigenfunctions of the Frobenius-Perron operator of the tent map
    • M. Dörfle, Spectrum and eigenfunctions of the Frobenius-Perron operator of the tent map. J. Stat. Phys. 40, 93-103 (1985).
    • (1985) J. Stat. Phys. , vol.40 , pp. 93-103
    • Dörfle, M.1
  • 20
    • 0346779701 scopus 로고
    • r-adic one dimensional maps and the Euler summation formula
    • P. Gaspard, r-adic one dimensional maps and the Euler summation formula. J. Phys. A 25, L483-485 (1992); Diffusion in uniformly hyperbolic one-dimensional maps and Appel polynomials. Phys. Lett. A 168, 13-17 (1992).
    • (1992) J. Phys. A , vol.25
    • Gaspard, P.1
  • 21
    • 0041336891 scopus 로고
    • Diffusion in uniformly hyperbolic one-dimensional maps and Appel polynomials
    • P. Gaspard, r-adic one dimensional maps and the Euler summation formula. J. Phys. A 25, L483-485 (1992); Diffusion in uniformly hyperbolic one-dimensional maps and Appel polynomials. Phys. Lett. A 168, 13-17 (1992).
    • (1992) Phys. Lett. A , vol.168 , pp. 13-17
  • 22
    • 0039892092 scopus 로고
    • Transport as a dynamical property of a simple map
    • H. H. Hasegawa and D. Driebe, Transport as a dynamical property of a simple map. Phys. Lett. A 168, 18-24 (1992); Spectral determination and physical conditions for a class of chaotic piecewise-linear maps. Ibid. 176, 193-201 (1993).
    • (1992) Phys. Lett. A , vol.168 , pp. 18-24
    • Hasegawa, H.H.1    Driebe, D.2
  • 23
    • 0039210307 scopus 로고
    • Spectral determination and physical conditions for a class of chaotic piecewise-linear maps
    • H. H. Hasegawa and D. Driebe, Transport as a dynamical property of a simple map. Phys. Lett. A 168, 18-24 (1992); Spectral determination and physical conditions for a class of chaotic piecewise-linear maps. Ibid. 176, 193-201 (1993).
    • (1993) Phys. Lett. A , vol.176 , pp. 193-201
  • 24
    • 0001853880 scopus 로고
    • Deterministic diffusion, De Rham equation and fractal eigenvectors
    • S. Tasaki, Z. Suchanecki and I. Antoniou, Deterministic diffusion, De Rham equation and fractal eigenvectors. Phys. Lett. A 179, 97-102 (1993); Ergodic properties of piecewise linear maps on fractal repellers. Ibid. 103-110; Spectral decomposition and fractal eigenvectors for a class of piecewise linear maps. Chaos, Solitons & Fractals 4, 227-254 (1994).
    • (1993) Phys. Lett. A , vol.179 , pp. 97-102
    • Tasaki, S.1    Suchanecki, Z.2    Antoniou, I.3
  • 25
    • 0001712429 scopus 로고    scopus 로고
    • Ergodic properties of piecewise linear maps on fractal repellers
    • S. Tasaki, Z. Suchanecki and I. Antoniou, Deterministic diffusion, De Rham equation and fractal eigenvectors. Phys. Lett. A 179, 97-102 (1993); Ergodic properties of piecewise linear maps on fractal repellers. Ibid. 103-110; Spectral decomposition and fractal eigenvectors for a class of piecewise linear maps. Chaos, Solitons & Fractals 4, 227-254 (1994).
    • Phys. Lett. A , pp. 103-110
  • 26
    • 0028378242 scopus 로고
    • Spectral decomposition and fractal eigenvectors for a class of piecewise linear maps
    • S. Tasaki, Z. Suchanecki and I. Antoniou, Deterministic diffusion, De Rham equation and fractal eigenvectors. Phys. Lett. A 179, 97-102 (1993); Ergodic properties of piecewise linear maps on fractal repellers. Ibid. 103-110; Spectral decomposition and fractal eigenvectors for a class of piecewise linear maps. Chaos, Solitons & Fractals 4, 227-254 (1994).
    • (1994) Chaos, Solitons & Fractals , vol.4 , pp. 227-254
  • 27
    • 24844433149 scopus 로고
    • Generalized Markov coarse graining and spectral decompositions of chaotic piecewise linear maps
    • D. Mackernan and G. Nicolis, Generalized Markov coarse graining and spectral decompositions of chaotic piecewise linear maps. Phys. Rev. E 50, 988-999 (1994).
    • (1994) Phys. Rev. E , vol.50 , pp. 988-999
    • Mackernan, D.1    Nicolis, G.2
  • 28
    • 0000910627 scopus 로고    scopus 로고
    • Spectral decomposition of the tent maps and the isomorphism of dynamical systems
    • I. Antoniou and Bi Qiao, Spectral decomposition of the tent maps and the isomorphism of dynamical systems. Phys. Lett. A 215, 280-290 (1996).
    • (1996) Phys. Lett. A , vol.215 , pp. 280-290
    • Antoniou, I.1    Qiao, B.2
  • 29
    • 13544256739 scopus 로고    scopus 로고
    • Jordan blocks in a one-dimensional Markov map
    • in press
    • D. Driebe, Jordan blocks in a one-dimensional Markov map. Comput. Math. Appl. (in press); D. Driebe and G. Ordouez, Using symmetries of the Frobenius-Perron operator to determine spectral decompositions. Phys. Lett. A 211, 204-210 (1996).
    • Comput. Math. Appl.
    • Driebe, D.1
  • 30
    • 13544256739 scopus 로고    scopus 로고
    • Using symmetries of the Frobenius-Perron operator to determine spectral decompositions
    • D. Driebe, Jordan blocks in a one-dimensional Markov map. Comput. Math. Appl. (in press); D. Driebe and G. Ordouez, Using symmetries of the Frobenius-Perron operator to determine spectral decompositions. Phys. Lett. A 211, 204-210 (1996).
    • (1996) Phys. Lett. A , vol.211 , pp. 204-210
    • Driebe, D.1    Ordouez, G.2
  • 31
    • 85033121054 scopus 로고    scopus 로고
    • Resonances of dynamical systems and Fredholm-Riesz operators in rigged Hubert spaces
    • in press
    • O. Bandtlow, I. Antoniou and Z. Suchanecki, Resonances of dynamical systems and Fredholm-Riesz operators in rigged Hubert spaces. Comput. Math. Appl. (in press).
    • Comput. Math. Appl.
    • Bandtlow, O.1    Antoniou, I.2    Suchanecki, Z.3
  • 36
    • 0000917444 scopus 로고
    • Intrinsic irreversibility and integrability of dynamics
    • I. Antoniou and I. Prigogine, Intrinsic irreversibility and integrability of dynamics. Physica A 192, 443-464 (1993).
    • (1993) Physica A , vol.192 , pp. 443-464
    • Antoniou, I.1    Prigogine, I.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.