메뉴 건너뛰기




Volumn 28, Issue 4, 2006, Pages 1275-1288

Efficient detection of periodic orbits in chaotic systems by stabilizing transformations

Author keywords

Coupled H non maps; Kicked double rotor map; Unstable periodic orbits

Indexed keywords

ALGORITHMS; EULER EQUATIONS; ITERATIVE METHODS; MATHEMATICAL TRANSFORMATIONS; SET THEORY;

EID: 34547187008     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/050623401     Document Type: Article
Times cited : (13)

References (26)
  • 1
    • 0001452580 scopus 로고
    • Characterization of unstable periodic orbits in chaotic attractors and repellers
    • O. BIHAM AND W. WENZEL, Characterization of unstable periodic orbits in chaotic attractors and repellers, Phys. Rev. Lett., 63 (1989), pp. 819-822.
    • (1989) Phys. Rev. Lett , vol.63 , pp. 819-822
    • BIHAM, O.1    WENZEL, W.2
  • 2
    • 0031272384 scopus 로고    scopus 로고
    • Coding, channel capacity, and noise resistance in communicating with chaos
    • E. M. BOLLT, Y.-C. LAI, AND C. GREBOGI, Coding, channel capacity, and noise resistance in communicating with chaos, Phys. Rev. Lett., 79 (1997), pp. 3787-3790.
    • (1997) Phys. Rev. Lett , vol.79 , pp. 3787-3790
    • BOLLT, E.M.1    LAI, Y.-C.2    GREBOGI, C.3
  • 3
    • 44949273254 scopus 로고
    • Periodic orbits as the skeleton of classical and quantum chaos
    • P. CVITANOVIĆ, Periodic orbits as the skeleton of classical and quantum chaos, Phys. D, 51 (1991), pp. 138-151.
    • (1991) Phys. D , vol.51 , pp. 138-151
    • CVITANOVIĆ, P.1
  • 4
    • 0001611630 scopus 로고    scopus 로고
    • Efficient algorithm for detecting unstable periodic orbits in chaotic systems
    • R. L. DAVIDCHACK AND Y.-C. LAI, Efficient algorithm for detecting unstable periodic orbits in chaotic systems, Phys. Rev. E (3), 60 (1999), pp. 6172-6175.
    • (1999) Phys. Rev. E , vol.60 , Issue.3 , pp. 6172-6175
    • DAVIDCHACK, R.L.1    LAI, Y.-C.2
  • 5
    • 0001167045 scopus 로고    scopus 로고
    • Estimating generating partitions of chaotic systems by unstable periodic orbits
    • R. L. DAVIDCHACK, Y.-C. LAI, E. M. BOLLT, AND M. DHAMALA, Estimating generating partitions of chaotic systems by unstable periodic orbits, Phys. Rev. E (3), 61 (2000), pp. 1353-1356.
    • (2000) Phys. Rev. E , vol.61 , Issue.3 , pp. 1353-1356
    • DAVIDCHACK, R.L.1    LAI, Y.-C.2    BOLLT, E.M.3    DHAMALA, M.4
  • 6
    • 0035920641 scopus 로고    scopus 로고
    • Towards complete detection of unstable periodic orbits in chaotic systems
    • R. L. DAVIDCHACK, Y.-C. LAI, A. KLEBANOFF, AND E. M. BOLLT, Towards complete detection of unstable periodic orbits in chaotic systems, Phys. Lett. A, 287 (2001), pp. 99-104.
    • (2001) Phys. Lett. A , vol.287 , pp. 99-104
    • DAVIDCHACK, R.L.1    LAI, Y.-C.2    KLEBANOFF, A.3    BOLLT, E.M.4
  • 8
    • 0035438230 scopus 로고    scopus 로고
    • Interval methods for rigorous investigations of periodic orbits
    • Z. GALIAS, Interval methods for rigorous investigations of periodic orbits, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 11 (2001), pp. 2427-2450.
    • (2001) Internat. J. Bifur. Chaos Appl. Sci. Engrg , vol.11 , pp. 2427-2450
    • GALIAS, Z.1
  • 11
    • 26544432046 scopus 로고
    • Alternative method to find orbits in chaotic systems
    • K. T. HANSEN, Alternative method to find orbits in chaotic systems, Phys. Rev. E (3), 52 (1995), pp. 2388-2391.
    • (1995) Phys. Rev. E , vol.52 , Issue.3 , pp. 2388-2391
    • HANSEN, K.T.1
  • 12
    • 0004151494 scopus 로고
    • Cambridge University Press, Cambridge, UK
    • R. A. HORN AND C. R. JOHNSON, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985.
    • (1985) Matrix Analysis
    • HORN, R.A.1    JOHNSON, C.R.2
  • 15
    • 0034819197 scopus 로고    scopus 로고
    • Convergence analysis of Davidchack and Lai's algorithm for finding periodic orbits
    • A. KLEBANOFF AND E. M. BOLLT, Convergence analysis of Davidchack and Lai's algorithm for finding periodic orbits, Chaos Solitons Fractals, 12 (2001), pp. 1305-1322.
    • (2001) Chaos Solitons Fractals , vol.12 , pp. 1305-1322
    • KLEBANOFF, A.1    BOLLT, E.M.2
  • 16
    • 4143093387 scopus 로고
    • Characterization of an experimental strange attractor by periodic orbits
    • D. P. LATHROP AND E. J. KOSTELICH, Characterization of an experimental strange attractor by periodic orbits, Phys. Rev. A (3), 40 (1989), pp. 4028-4031.
    • (1989) Phys. Rev. A , vol.40 , Issue.3 , pp. 4028-4031
    • LATHROP, D.P.1    KOSTELICH, E.J.2
  • 17
    • 0001639797 scopus 로고    scopus 로고
    • An adaptive Newton-Picard algorithm with subspace iteration for computing periodic solutions
    • K. LUST, D. ROOSE, A. SPENCE, AND A. R. CHAMPNEYS, An adaptive Newton-Picard algorithm with subspace iteration for computing periodic solutions, SIAM J. Sci. Comput., 19 (1998), pp. 1188-1209.
    • (1998) SIAM J. Sci. Comput , vol.19 , pp. 1188-1209
    • LUST, K.1    ROOSE, D.2    SPENCE, A.3    CHAMPNEYS, A.R.4
  • 18
    • 0347948959 scopus 로고    scopus 로고
    • Finding all periodic orbits of maps using Newton methods: Sizes of basins
    • J. R. MILLER AND J. A. YORKE, Finding all periodic orbits of maps using Newton methods: Sizes of basins, Phys. D, 135 (2000), pp. 195-211.
    • (2000) Phys. D , vol.135 , pp. 195-211
    • MILLER, J.R.1    YORKE, J.A.2
  • 19
    • 0003582543 scopus 로고
    • Cambridge University Press, Cambridge, UK
    • E. OTT, Chaos in Dynamical Systems, Cambridge University Press, Cambridge, UK, 1993.
    • (1993) Chaos in Dynamical Systems
    • OTT, E.1
  • 21
    • 7444240810 scopus 로고    scopus 로고
    • Stability transformation: A tool to solve nonlinear problems
    • D. PINGEL, P. SCHMELCHER, AND F. K. DIAKONOS, Stability transformation: A tool to solve nonlinear problems, Phys. Rep., 400 (2004), pp. 67-148.
    • (2004) Phys. Rep , vol.400 , pp. 67-148
    • PINGEL, D.1    SCHMELCHER, P.2    DIAKONOS, F.K.3
  • 22
    • 0034300276 scopus 로고    scopus 로고
    • From template analysis to generating partitions I: Periodic orbits, knots, and symbolic encodings
    • J. PLUMECOQ AND M. LEFRANC, From template analysis to generating partitions I: Periodic orbits, knots, and symbolic encodings, Phys. D, 144 (2000), pp. 231-258.
    • (2000) Phys. D , vol.144 , pp. 231-258
    • PLUMECOQ, J.1    LEFRANC, M.2
  • 23
    • 0008518824 scopus 로고
    • Towards a statistical mechanics of spatiotemporal chaos
    • A. POLITI AND A. TORCINI, Towards a statistical mechanics of spatiotemporal chaos, Phys. Rev. Lett., 69 (1992), pp. 3421-3424.
    • (1992) Phys. Rev. Lett , vol.69 , pp. 3421-3424
    • POLITI, A.1    TORCINI, A.2
  • 25
    • 6144249748 scopus 로고    scopus 로고
    • Detecting unstable periodic orbits of chaotic dynamical systems
    • P. SCHMELCHER AND F. K. DIAKONOS, Detecting unstable periodic orbits of chaotic dynamical systems, Phys. Rev. Lett., 78 (1997), pp. 4733-4736.
    • (1997) Phys. Rev. Lett , vol.78 , pp. 4733-4736
    • SCHMELCHER, P.1    DIAKONOS, F.K.2
  • 26
    • 0032025560 scopus 로고    scopus 로고
    • General approach to the localization of unstable periodic orbits in chaotic dynamical systems
    • P. SCHMELCHER AND F. K. DIAKONOS, General approach to the localization of unstable periodic orbits in chaotic dynamical systems, Phys. Rev. E (3), 57 (1998), pp. 2739-2746.
    • (1998) Phys. Rev. E , vol.57 , Issue.3 , pp. 2739-2746
    • SCHMELCHER, P.1    DIAKONOS, F.K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.