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Volumn 4, Issue 3, 2005, Pages 515-562

Symbolic codes for rotational orbits

Author keywords

Anti integrable limit; Area preserving H non mapping; Partition; Smale horseshoe; Symbol sequence

Indexed keywords

AREA-PRESERVING HÉNON MAPPING; PARTITION; SMALE HORSESHOE; SYMBOLIC SEQUENCES;

EID: 33644892552     PISSN: 15360040     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/040612877     Document Type: Article
Times cited : (13)

References (48)
  • 3
    • 0012643993 scopus 로고    scopus 로고
    • Applied symbolic dynamics and chaos
    • World Scientific, River Edge, NJ
    • B.-L. HAO AND W.-M. ZHENG, Applied Symbolic Dynamics and Chaos, Dir. Chaos 7, World Scientific, River Edge, NJ, 1998.
    • (1998) Dir. Chaos , vol.7
    • Hao, B.-L.1    Zheng, W.-M.2
  • 4
    • 0348225591 scopus 로고    scopus 로고
    • Homoclinic bifurcations for the Hénon map
    • D. STERLING, H. R. DULLIN, AND J. D. MEISS, Homoclinic bifurcations for the Hénon map, Phys. D, 134 (1999), pp. 153-184.
    • (1999) Phys. D , vol.134 , pp. 153-184
    • Sterling, D.1    Dullin, H.R.2    Meiss, J.D.3
  • 5
    • 0001039322 scopus 로고
    • Numerical study of quadratic area-preserving mappings
    • M. HÉNON, Numerical study of quadratic area-preserving mappings, Quart. Appl. Math., 27 (1969), pp. 291-312.
    • (1969) Quart. Appl. Math. , vol.27 , pp. 291-312
    • Hénon, M.1
  • 6
    • 0000148713 scopus 로고
    • Chaotic trajectories in the standard map, the concept of anti-integrability
    • S. AUBRY AND G. ABRAMOVICI, Chaotic trajectories in the standard map, the concept of anti-integrability, Phys. D, 43 (1990), pp. 199-219.
    • (1990) Phys. D , vol.43 , pp. 199-219
    • Aubry, S.1    Abramovici, G.2
  • 7
    • 0002072428 scopus 로고
    • Coexistence of cycles of a continuous map of a line into itself
    • A. N. SARKOVSKII, Coexistence of cycles of a continuous map of a line into itself, Ukrain. Mat. Z., 16 (1964), pp. 61-71.
    • (1964) Ukrain. Mat. Z. , vol.16 , pp. 61-71
    • Sarkovskii, A.N.1
  • 9
    • 0002591468 scopus 로고
    • A two-dimensional mapping with a strange attractor
    • M. HÉNON, A two-dimensional mapping with a strange attractor, Comm. Math. Phys., 50 (1976), pp. 69-77.
    • (1976) Comm. Math. Phys. , vol.50 , pp. 69-77
    • Hénon, M.1
  • 10
    • 0039659690 scopus 로고
    • Generating partitions for the dissipative Hénon map
    • P. GRASSBERGER AND H. KANTZ, Generating partitions for the dissipative Hénon map, Phys. Lett. A, 113 (1985), pp. 235-238.
    • (1985) Phys. Lett. A , vol.113 , pp. 235-238
    • Grassberger, P.1    Kantz, H.2
  • 11
    • 5544234625 scopus 로고
    • Topological and metric properties of Hénon-type strange attractors
    • P. CVITANOVIC, G. H. GUNARATNE, AND I. PROCACCIA, Topological and metric properties of Hénon-type strange attractors, Phys. Rev. A (3), 38 (1988), pp. 1503-1520.
    • (1988) Phys. Rev. A (3) , vol.38 , pp. 1503-1520
    • Cvitanovic, P.1    Gunaratne, G.H.2    Procaccia, I.3
  • 12
    • 0001935355 scopus 로고
    • Remarks on the symbolic dynamics for the Hénon map
    • K. T. HANSEN, Remarks on the symbolic dynamics for the Hénon map, Phys. Lett. A, 165 (1992), pp. 100-104.
    • (1992) Phys. Lett. A , vol.165 , pp. 100-104
    • Hansen, K.T.1
  • 13
    • 0000814505 scopus 로고
    • Generating partitions in Hénon-type maps
    • F. GIOVANNINl AND A. POLITI, Generating partitions in Hénon-type maps, Phys. Lett. A, 161 (1992), pp. 332-336.
    • (1992) Phys. Lett. A , vol.161 , pp. 332-336
    • Giovanninl, F.1    Politi, A.2
  • 14
    • 21344479849 scopus 로고
    • Dynamics for a two-dimensional antisymmetric map
    • H. P. FANG, Dynamics for a two-dimensional antisymmetric map, J. Phys. A, 27 (1994), pp. 5187-5200.
    • (1994) J. Phys. A , vol.27 , pp. 5187-5200
    • Fang, H.P.1
  • 15
    • 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
  • 16
    • 0041783263 scopus 로고    scopus 로고
    • Computing periodic orbits using the anti-integrable limit
    • D. STERLING AND J. D. MEISS, Computing periodic orbits using the anti-integrable limit, Phys. Lett. A, 241 (1998), pp. 46-52.
    • (1998) Phys. Lett. A , vol.241 , pp. 46-52
    • Sterling, D.1    Meiss, J.D.2
  • 17
    • 36149031123 scopus 로고
    • On the symbolic dynamics of the Hénon map
    • P. GRASSBERGER, H. KANTZ, AND U. MOENIG, On the symbolic dynamics of the Hénon map, J. Phys. A, 22 (1989), pp. 5217-5230.
    • (1989) J. Phys. A , vol.22 , pp. 5217-5230
    • Grassberger, P.1    Kantz, H.2    Moenig, U.3
  • 18
    • 0040560227 scopus 로고    scopus 로고
    • Bifurcation structures in maps of Hénon type
    • K. T. HANSEN AND P. CVITANOVIC, Bifurcation structures in maps of Hénon type, Nonlinearity, 11 (1998), pp. 1233-1261.
    • (1998) Nonlinearity , vol.11 , pp. 1233-1261
    • Hansen, K.T.1    Cvitanovic, P.2
  • 19
    • 24244472693 scopus 로고
    • Generating partition for the standard map
    • F. CHRISTIANSEN AND A. POLITI, Generating partition for the standard map, Phys. Rev. E (3), 51 (1995), pp. R3811-R3814.
    • (1995) Phys. Rev. E (3) , vol.51
    • Christiansen, F.1    Politi, A.2
  • 20
    • 0002242403 scopus 로고    scopus 로고
    • Guidelines for the construction of a generating partition in the standard map
    • F. CHRISTIANSEN AND A. POLITI, Guidelines for the construction of a generating partition in the standard map, Phys. D, 109 (1997), pp. 32-41.
    • (1997) Phys. D , vol.109 , pp. 32-41
    • Christiansen, F.1    Politi, A.2
  • 21
    • 0343040265 scopus 로고    scopus 로고
    • Symbolic encoding in symplectic maps
    • F. CHRISTIANSEN AND A. POLITI, Symbolic encoding in symplectic maps, Nonlinearity, 9 (1996), pp. 1623-1640.
    • (1996) Nonlinearity , vol.9 , pp. 1623-1640
    • Christiansen, F.1    Politi, A.2
  • 22
    • 0000089306 scopus 로고
    • Symbolic dynamics and rotation numbers
    • P. VEERMAN, Symbolic dynamics and rotation numbers, Phys. A, 134 (1986), pp. 543-576.
    • (1986) Phys. A , vol.134 , pp. 543-576
    • Veerman, P.1
  • 23
    • 0000177877 scopus 로고
    • Symbolic dynamics for the circle map
    • W.-M. ZHENG, Symbolic dynamics for the circle map, Internat. J. Modern Phys. B, 5 (1991), pp. 481-495.
    • (1991) Internat. J. Modern Phys. B , vol.5 , pp. 481-495
    • Zheng, W.-M.1
  • 24
    • 0001429903 scopus 로고
    • A linear code for the sawtooth and cat maps
    • I. C. PERCIVAL AND F. VIVALDI, A linear code for the sawtooth and cat maps, Phys. D, 27 (1987), pp. 373-386.
    • (1987) Phys. D , vol.27 , pp. 373-386
    • Percival, I.C.1    Vivaldi, F.2
  • 25
    • 0001229841 scopus 로고
    • Class renormalization: Islands around islands
    • J. D. MEISS, Class renormalization: Islands around islands, Phys. Rev. A (3), 34 (1986), pp. 2375-2383.
    • (1986) Phys. Rev. A (3) , vol.34 , pp. 2375-2383
    • Meiss, J.D.1
  • 26
    • 0005324116 scopus 로고
    • Symbolic dynamics approach to the two-D chaos in area-preserving maps
    • Y. AIZAWA, Symbolic dynamics approach to the two-D chaos in area-preserving maps, Progr. Theoret. Phys., 71 (1984), pp. 1419-1421.
    • (1984) Progr. Theoret. Phys. , vol.71 , pp. 1419-1421
    • Aizawa, Y.1
  • 27
    • 0034178818 scopus 로고    scopus 로고
    • Symbolic dynamics for sticky sets in Hamiltonian systems
    • V. AFRAIMOVICH, A. MAASS, AND J. URAS, Symbolic dynamics for sticky sets in Hamiltonian systems, Nonlinearity, 13 (2000), pp. 617-637.
    • (2000) Nonlinearity , vol.13 , pp. 617-637
    • Afraimovich, V.1    Maass, A.2    Uras, J.3
  • 28
    • 46149130013 scopus 로고
    • Markov tree model of transport in area preserving maps
    • J. D. MEISS AND E. OTT, Markov tree model of transport in area preserving maps, Phys. D, 20 (1986), pp. 387-402.
    • (1986) Phys. D , vol.20 , pp. 387-402
    • Meiss, J.D.1    Ott, E.2
  • 29
    • 0038805190 scopus 로고
    • Renormalisation in area-preserving maps
    • World Scientific, River Edge, NJ
    • R. S. MACKAY, Renormalisation in Area-Preserving Maps, Adv. Ser. Nonlinear Dynam. 6, World Scientific, River Edge, NJ, 1993.
    • (1993) Adv. Ser. Nonlinear Dynam. , vol.6
    • Mackay, R.S.1
  • 30
    • 0010890055 scopus 로고
    • Symplectic maps, variational principles, and transport
    • J. D. MEISS, Symplectic maps, variational principles, and transport, Rev. Modern Phys., 64 (1992), pp. 795-848.
    • (1992) Rev. Modern Phys. , vol.64 , pp. 795-848
    • Meiss, J.D.1
  • 31
  • 32
    • 0000671077 scopus 로고
    • Shift automorphisms in the Hénon mapping
    • R. L. DEVANEY AND Z. NITECKI, Shift automorphisms in the Hénon mapping, Comm. Math. Phys., 67 (1979), pp. 137-146.
    • (1979) Comm. Math. Phys. , vol.67 , pp. 137-146
    • Devaney, R.L.1    Nitecki, Z.2
  • 33
    • 0002544793 scopus 로고
    • The concept of anti-integrability: Definition, theorems and applications to the standard map
    • Twist Mappings and Their Applications, R. McGehee and K. R. Meyer, eds., Springer-Verlag, New York
    • S. J. AUBRY, The concept of anti-integrability: Definition, theorems and applications to the standard map, in Twist Mappings and Their Applications, R. McGehee and K. R. Meyer, eds., IMA Vol. Math. Appl. 44, Springer-Verlag, New York, 1992, pp. 7-54.
    • (1992) IMA Vol. Math. Appl. , vol.44 , pp. 7-54
    • Aubry, S.J.1
  • 34
    • 0003582535 scopus 로고
    • Introduction to the theory of hamiltonian systems
    • Springer-Verlag, New York
    • K. R. MEYER AND G. R. HALL, Introduction to the Theory of Hamiltonian Systems, Appl. Math. Sci. 90, Springer-Verlag, New York, 1992.
    • (1992) Appl. Math. Sci. , vol.90
    • Meyer, K.R.1    Hall, G.R.2
  • 35
    • 51249175593 scopus 로고
    • Periodic points and rotation numbers for area-preserving diffeomorphisms of the plane
    • J. FRANKS, Periodic points and rotation numbers for area-preserving diffeomorphisms of the plane, Inst. Hautes Études Sci. Publ. Math., 71 (1990), pp. 105-120.
    • (1990) Inst. Hautes Études Sci. Publ. Math. , vol.71 , pp. 105-120
    • Franks, J.1
  • 36
    • 51249166490 scopus 로고
    • On quadratic symplectic mappings
    • J. K. MOSER, On quadratic symplectic mappings, Math. Z., 216 (1994), pp. 417-430.
    • (1994) Math. Z. , vol.216 , pp. 417-430
    • Moser, J.K.1
  • 37
    • 48749143267 scopus 로고
    • The discrete Frenkel-Kontorova model and its extensions
    • S. AUBRY AND P. Y. LE DAERON, The discrete Frenkel-Kontorova model and its extensions, Phys. D, 8 (1983), pp. 381-422.
    • (1983) Phys. D , vol.8 , pp. 381-422
    • Aubry, S.1    Le Daeron, P.Y.2
  • 38
    • 0039269070 scopus 로고    scopus 로고
    • Symbolic dynamics and periodic orbits for the cardioid billiard
    • A. BÄCKER AND H. R. DULLIN, Symbolic dynamics and periodic orbits for the cardioid billiard, J. Phys. A, 30 (1997), pp. 1991-2020.
    • (1997) J. Phys. A , vol.30 , pp. 1991-2020
    • Bäcker, A.1    Dullin, H.R.2
  • 39
    • 0034300282 scopus 로고    scopus 로고
    • Self-rotation number using the turning angle
    • H. R. DULLIN, D. STERLING, AND J. D. MEISS, Self-rotation number using the turning angle, Phys. D, 145 (2000), pp. 25-46.
    • (2000) Phys. D , vol.145 , pp. 25-46
    • Dullin, H.R.1    Sterling, D.2    Meiss, J.D.3
  • 41
    • 0002569105 scopus 로고    scopus 로고
    • Time-reversal symmetry in dynamical systems: A survey
    • J. W. S. LAMB AND J. A. G. ROBERTS, Time-reversal symmetry in dynamical systems: A survey, Phys. D, 112 (1998), pp. 1-39.
    • (1998) Phys. D , vol.112 , pp. 1-39
    • Lamb, J.W.S.1    Roberts, J.A.G.2
  • 42
    • 0043158712 scopus 로고
    • Intersection properties of invariant manifolds in certain twist maps
    • J. J. P. VEERMAN AND F. M. TANGERMAN, Intersection properties of invariant manifolds in certain twist maps, Comm. Math. Phys., 139 (1991), pp. 245-265.
    • (1991) Comm. Math. Phys. , vol.139 , pp. 245-265
    • Veerman, J.J.P.1    Tangerman, F.M.2
  • 43
    • 0039592690 scopus 로고    scopus 로고
    • Generalized Hénon maps: The cubic diffeomorphisms of the plane
    • H. R. DULLIN AND J. D. MEISS, Generalized Hénon maps: The cubic diffeomorphisms of the plane, Phys. D, 143 (2000), pp. 265-292.
    • (2000) Phys. D , vol.143 , pp. 265-292
    • Dullin, H.R.1    Meiss, J.D.2
  • 44
    • 2442719195 scopus 로고    scopus 로고
    • Reversors and symmetries for polynomial automorphisms of the complex plane
    • A. GÓMEZ AND J. D. MEISS, Reversors and symmetries for polynomial automorphisms of the complex plane, Nonlinearity, 17 (2004), pp. 975-1000.
    • (2004) Nonlinearity , vol.17 , pp. 975-1000
    • Gómez, A.1    Meiss, J.D.2
  • 45
    • 0000412724 scopus 로고
    • Arithmetical properties of strongly chaotic motion
    • I. C. PERCIVAL AND F. VIVALDI, Arithmetical properties of strongly chaotic motion, Phys. D, 25 (1987), pp. 105-130.
    • (1987) Phys. D , vol.25 , pp. 105-130
    • Percival, I.C.1    Vivaldi, F.2
  • 46
    • 4243465975 scopus 로고
    • Orbit extension methods for finding unstable orbits
    • Q. CHEN, J. D. MEISS, AND I. C. PERCIVAL, Orbit extension methods for finding unstable orbits, Phys. D, 29 (1987), pp. 143-154.
    • (1987) Phys. D , vol.29 , pp. 143-154
    • Chen, Q.1    Meiss, J.D.2    Percival, I.C.3
  • 47


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