메뉴 건너뛰기




Volumn 240, Issue 8, 2011, Pages 732-753

Dynamics in chaotic zones of area preserving maps: Close to separatrix and global instability zones

Author keywords

Area preserving maps; Chaotic zones; Dynamical systems; Return models

Indexed keywords

DYNAMICAL SYSTEMS; STOCHASTIC SYSTEMS;

EID: 79951518121     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2010.12.005     Document Type: Article
Times cited : (16)

References (49)
  • 1
    • 10044277502 scopus 로고
    • Homoclinic tanglesclassification and applications
    • V. Rom Kedar Homoclinic tanglesclassification and applications Nonlinearity 7 1994 441 473
    • (1994) Nonlinearity , vol.7 , pp. 441-473
    • Rom Kedar, V.1
  • 2
    • 0001585893 scopus 로고
    • Stochastic instability of trapped particles and conditions of applicability of the quasi-linear approximation
    • G.M. Zaslavsky, and N.N. Filonenko Stochastic instability of trapped particles and conditions of applicability of the quasi-linear approximation Sov. Phys. JETP 27 1968 851 857
    • (1968) Sov. Phys. JETP , vol.27 , pp. 851-857
    • Zaslavsky, G.M.1    Filonenko, N.N.2
  • 3
    • 0012097571 scopus 로고
    • A universal instability of many-dimensional oscillator system
    • B.V. Chirikov A universal instability of many-dimensional oscillator system Phys. Rep. 52 1979 264 379
    • (1979) Phys. Rep. , vol.52 , pp. 264-379
    • Chirikov, B.V.1
  • 4
    • 0010890055 scopus 로고
    • Symplectic maps, variational principles, and transport
    • J.D. Meiss Symplectic maps, variational principles, and transport Rev. Modern Phys. 64 3 1992
    • (1992) Rev. Modern Phys. , vol.64 , Issue.3
    • Meiss, J.D.1
  • 5
    • 34548319442 scopus 로고    scopus 로고
    • Separatrix maps in Hamiltonian systems
    • G.N. Piftankin, and D.V. Treschev Separatrix maps in Hamiltonian systems Russian Math. Surveys 2 62 2007 219 322
    • (2007) Russian Math. Surveys , vol.2 , Issue.62 , pp. 219-322
    • Piftankin, G.N.1    Treschev, D.V.2
  • 6
    • 0000940010 scopus 로고
    • Transient measures in the standard map
    • J.D. Meiss Transient measures in the standard map Physica D 74 1994 254 267
    • (1994) Physica D , vol.74 , pp. 254-267
    • Meiss, J.D.1
  • 7
    • 0003292012 scopus 로고
    • Stable and Random Motions in Dynamical Systems
    • Princeton Univ. Press Princeton, NY
    • J. Moser Stable and Random Motions in Dynamical Systems Annals of Mathematical Studies vol. 77 1973 Princeton Univ. Press Princeton, NY
    • (1973) Annals of Mathematical Studies , vol.77
    • Moser, J.1
  • 8
    • 79951517571 scopus 로고    scopus 로고
    • Dynamical description of the domain of stability of area preserving maps
    • C. Sim, A. Vieiro, Dynamical description of the domain of stability of area preserving maps, Work in Progress, 2010.
    • (2010) Work in Progress
    • C. Simó1
  • 9
    • 67049122157 scopus 로고    scopus 로고
    • Resonant zones, inner and outer splittings in generic and low order resonances of area preserving maps
    • C. Sim, and A. Vieiro Resonant zones, inner and outer splittings in generic and low order resonances of area preserving maps Nonlinearity 22 5 2009 1191 1245
    • (2009) Nonlinearity , vol.22 , Issue.5 , pp. 1191-1245
    • Sim, C.1    Vieiro, A.2
  • 10
    • 0030355090 scopus 로고    scopus 로고
    • Invariant circles in the BogdanovTakens bifurcation for diffeomorphisms
    • H. Broer, R. Roussarie, and C. Sim Invariant circles in the BogdanovTakens bifurcation for diffeomorphisms Ergodic Theory Dynam. Systems 16 1996 1147 1172
    • (1996) Ergodic Theory Dynam. Systems , vol.16 , pp. 1147-1172
    • Broer, H.1    Roussarie, R.2    Sim, C.3
  • 11
    • 0021660205 scopus 로고
    • The separation of motions in systems with rapidly rotating phase
    • DOI 10.1016/0021-8928(84)90078-9
    • A. Neishtadt The separation of motions in systems with rapidly rotating phase Prikl. Mat. Mekh. 48 1984 133 139 (Pubitemid 15587176)
    • (1984) Journal of Applied Mathematics and Mechanics , vol.48 , Issue.2 , pp. 133-139
    • Neishtadt, A.I.1
  • 12
    • 84971996008 scopus 로고
    • The splitting of separatrices for analytic diffeomorphisms
    • E. Fontich, and C. Sim The splitting of separatrices for analytic diffeomorphisms Ergodic Theory Dynam. Systems 10 1990 295 318
    • (1990) Ergodic Theory Dynam. Systems , vol.10 , pp. 295-318
    • Fontich, E.1    Sim, C.2
  • 13
    • 0002439526 scopus 로고
    • A refined formula for the separatrix splitting for the standard map
    • V. Gelfreich, V.F. Lazutkin, and N.V. Svanidze A refined formula for the separatrix splitting for the standard map Physica D 71 12 1994 82 101
    • (1994) Physica D , vol.71 , Issue.12 , pp. 82-101
    • Gelfreich, V.1    Lazutkin, V.F.2    Svanidze, N.V.3
  • 14
    • 0035600465 scopus 로고    scopus 로고
    • Splitting of separatrices: Perturbation theory and exponential smallness
    • V. Gelfreich, and V.F. Lazutkin Splitting of separatrices: perturbation theory and exponential smallness Russian Math. Surveys 56 3 2001 499 558
    • (2001) Russian Math. Surveys , vol.56 , Issue.3 , pp. 499-558
    • Gelfreich, V.1    Lazutkin, V.F.2
  • 15
    • 0031236892 scopus 로고    scopus 로고
    • Hidden renormalization group for the near-separatrix Hamiltonian dynamics
    • PII S0370157397000379
    • L. Kuznesov, and G.M. Zaslavsky Hidden renormalization group for the near-separatrix Hamiltonian dynamics Phys. Rep. 288 1997 457 485 (Pubitemid 127167705)
    • (1997) Physics Report , vol.288 , Issue.1-6 , pp. 457-485
    • Kuznetsov, L.1    Zaslavsky, G.M.2
  • 16
    • 5844271481 scopus 로고
    • Secondary homoclinic bifurcation theorems
    • V. Rom Kedar Secondary homoclinic bifurcation theorems Chaos 5 2 1994 385 401
    • (1994) Chaos , vol.5 , Issue.2 , pp. 385-401
    • Rom Kedar, V.1
  • 17
    • 37649026517 scopus 로고    scopus 로고
    • Scaling invariance of the homoclinic tangle
    • L. Kuznesov, and G.M. Zaslavsky Scaling invariance of the homoclinic tangle Phys. Rev. E 66 2002 1 7
    • (2002) Phys. Rev. e , vol.66 , pp. 1-7
    • Kuznesov, L.1    Zaslavsky, G.M.2
  • 18
    • 79951518346 scopus 로고    scopus 로고
    • Dynamics in a neighbourhood of separatrices of an area-preserving map
    • Chaos, Kinetics and Nonlinear Dynamics in FLuid and Plasmas Springer Berlin, Heidelberg
    • D. Treschev Dynamics in a neighbourhood of separatrices of an area-preserving map Chaos, Kinetics and Nonlinear Dynamics in FLuid and Plasmas Lecture Notes in Physics vol. 511 2007 Springer Berlin, Heidelberg 1 15
    • (2007) Lecture Notes in Physics , vol.511 , pp. 1-15
    • Treschev, D.1
  • 19
    • 0000789737 scopus 로고
    • Renormalization for stochastic layers
    • D.F. Escande Renormalization for stochastic layers Physica D 6 1982 119 125
    • (1982) Physica D , vol.6 , pp. 119-125
    • Escande, D.F.1
  • 20
    • 0006963160 scopus 로고    scopus 로고
    • Towards global models near homoclinic tangencies of dissipative diffeomorphisms
    • H. Broer, C. Sim, and J.C. Tatjer Towards global models near homoclinic tangencies of dissipative diffeomorphisms Nonlinearity 11 1998 667 770
    • (1998) Nonlinearity , vol.11 , pp. 667-770
    • Broer, H.1    Sim, C.2    Tatjer, J.C.3
  • 21
    • 78650695947 scopus 로고    scopus 로고
    • Planar radial weakly-dissipative diffeomorphisms
    • in press (doi:10.1063/1.3515168)̀
    • C. Sim, A. Vieiro, Planar radial weakly-dissipative diffeomorphisms, Chaos 20 (4) (2010), in press (doi:10.1063/1.3515168 ).
    • (2010) Chaos , vol.20 , Issue.4
    • C. Simó1
  • 22
    • 73149116812 scopus 로고    scopus 로고
    • Stability islands in the vicinity of separatrices of near-integrable maps
    • C. Sim, and D.V. Treschev Stability islands in the vicinity of separatrices of near-integrable maps Discrete Contin. Dyn. Syst. Ser. B 10 23 2008 681 698
    • (2008) Discrete Contin. Dyn. Syst. Ser. B , vol.10 , Issue.23 , pp. 681-698
    • Sim, C.1    Treschev, D.V.2
  • 23
    • 0037862066 scopus 로고
    • Chaotic dynamics in Hamiltonian systems with divided phase space
    • Springer-Verlag
    • B.V. Chirikov Chaotic dynamics in Hamiltonian systems with divided phase space Proceedings of the Sitges Conference on Statistical Mechanics Lecture Notes in Physics. Dynamical Systems and Chaos vol. 179 1983 Springer-Verlag 29 46
    • (1983) Lecture Notes in Physics. Dynamical Systems and Chaos , vol.179 , pp. 29-46
    • Chirikov, B.V.1
  • 24
    • 0003340667 scopus 로고
    • An obstruction method for the destruction of invariant curves
    • C. Sim, and A. Olvera An obstruction method for the destruction of invariant curves Physica D 26 1987 181 192
    • (1987) Physica D , vol.26 , pp. 181-192
    • Sim, C.1    Olvera, A.2
  • 25
    • 0001039322 scopus 로고
    • Numerical study of quadratic maps
    • M. Hnon Numerical study of quadratic maps Quart. Appl. Math. XXVII 3 1969 291 311
    • (1969) Quart. Appl. Math. , vol.27 , Issue.3 , pp. 291-311
    • Hnon, M.1
  • 27
    • 79951513989 scopus 로고    scopus 로고
    • Some remarks on the abundance of stable periodic orbits inside homoclinic lobes
    • submitted for publication
    • C. Sim, A. Vieiro, Some remarks on the abundance of stable periodic orbits inside homoclinic lobes, Physica D, 2010 (submitted for publication).
    • (2010) Physica D
    • C. Simó1
  • 28
    • 54649083821 scopus 로고    scopus 로고
    • Invariant curves of perturbations of non twist integrable area preserving maps
    • C. Sim Invariant curves of perturbations of non twist integrable area preserving maps Regul. Chaotic Dyn. 3 1998 180 195
    • (1998) Regul. Chaotic Dyn. , vol.3 , pp. 180-195
    • Sim, C.1
  • 29
    • 0031063207 scopus 로고    scopus 로고
    • Homoclinic orbits in the complex domain
    • V.F. Lazutkin, and C. Sim Homoclinic orbits in the complex domain Int. J. Bifurcat. Chaos 7 1997 253 274
    • (1997) Int. J. Bifurcat. Chaos , vol.7 , pp. 253-274
    • Lazutkin, V.F.1    Sim, C.2
  • 30
    • 21544480029 scopus 로고    scopus 로고
    • Splitting of separatrices for the Chirikov standard map
    • DOI 10.1007/s10958-005-0219-7
    • V.F. Lazutkin Splitting of separatrices for the Chirikov standard map J. Math. Sci. 128 2 2005 2687 2705 Translation of V.F. Lazutkin, Preprint VINITI, No. 6372-84 (1984) (Pubitemid 40924386)
    • (2005) Journal of Mathematical Sciences , vol.128 , Issue.2 , pp. 2687-2705
    • Lazutkin, V.F.1
  • 31
    • 0024926295 scopus 로고
    • Splitting of separatrices for standard and semistandard mappings
    • DOI 10.1016/0167-2789(89)90065-1
    • V.F. Lazutkin, I.G. Shakhmanski, and M.B. Tabanov Splitting of separatrices for standard and semistandard mappings Physica D 40 2 1989 235 248 Translation of V.F. Lazutkin, Preprint VINITI, No. 4027-85 (1985) (Pubitemid 20659941)
    • (1989) Physica D: Nonlinear Phenomena , vol.40 , Issue.2 , pp. 235-248
    • Lazutkin, V.F.1    Schachmannski, I.G.2    Tabanov, M.B.3
  • 32
    • 0001947506 scopus 로고
    • Exponentially small splitting of separatrices, matching in the complex plane and Borel summation
    • V. Hakim, and K. Mallick Exponentially small splitting of separatrices, matching in the complex plane and Borel summation Nonlinearity 6 1 1993 57 70
    • (1993) Nonlinearity , vol.6 , Issue.1 , pp. 57-70
    • Hakim, V.1    Mallick, K.2
  • 33
    • 0000410138 scopus 로고    scopus 로고
    • Exponential asymptotic expansions and approximations of the unstable and stable manifolds of singularly perturbed systems with the Hnon map as an example
    • A. Tovbis, M. Tsuchiya, and C. Jaff Exponential asymptotic expansions and approximations of the unstable and stable manifolds of singularly perturbed systems with the Hnon map as an example Chaos 8 3 1998 665 681
    • (1998) Chaos , vol.8 , Issue.3 , pp. 665-681
    • Tovbis, A.1    Tsuchiya, M.2    Jaff, C.3
  • 34
    • 0033241455 scopus 로고    scopus 로고
    • A proof of the exponentially small transversality of the separatrices for the standard map
    • V. Gelfreich A proof of the exponentially small transversality of the separatrices for the standard map Comm. Math. Phys. 201 1 1999 155 216
    • (1999) Comm. Math. Phys. , vol.201 , Issue.1 , pp. 155-216
    • Gelfreich, V.1
  • 36
    • 0001542986 scopus 로고    scopus 로고
    • Near threshold anomalous transport in the standard map
    • R.B. White, and G.M. Zaslavsky Near threshold anomalous transport in the standard map Chaos 8 4 1998 758 767
    • (1998) Chaos , vol.8 , Issue.4 , pp. 758-767
    • White, R.B.1    Zaslavsky, G.M.2
  • 37
    • 0036680219 scopus 로고    scopus 로고
    • Dynamical traps
    • DOI 10.1016/S0167-2789(02)00516-X, PII S016727890200516X
    • G.M. Zaslavsky Dynamical traps Physica D 168169 2002 292 304 (Pubitemid 34802487)
    • (2002) Physica D: Nonlinear Phenomena , vol.168-169 , pp. 292-304
    • Zaslavsky, G.M.1
  • 38
    • 48749143267 scopus 로고
    • The discrete FrenkelKontorova model and its extensions. I. Exact results for the ground-states
    • S. Aubry, and P.Y. Le Daeron The discrete FrenkelKontorova model and its extensions. I. Exact results for the ground-states Physica D 8 3 1983 381 422
    • (1983) Physica D , vol.8 , Issue.3 , pp. 381-422
    • Aubry, S.1    Le Daeron, P.Y.2
  • 39
    • 0000456667 scopus 로고
    • Existence of quasiperiodic orbits for twist homeomorphisms of the annulus
    • J.N. Mather Existence of quasiperiodic orbits for twist homeomorphisms of the annulus Topology 21 4 1982 457 467
    • (1982) Topology , vol.21 , Issue.4 , pp. 457-467
    • Mather, J.N.1
  • 40
    • 0000328945 scopus 로고
    • Locally most robust circles and boundary circles for area-preserving maps
    • R.S. Mackay, and J. Stark Locally most robust circles and boundary circles for area-preserving maps Nonlinearity 5 1992 867 888
    • (1992) Nonlinearity , vol.5 , pp. 867-888
    • MacKay, R.S.1    Stark, J.2
  • 42
    • 0001634731 scopus 로고
    • Boundary circles for area-preserving maps
    • J.M. Greene, R.S. Mackay, and J. Stark Boundary circles for area-preserving maps Physica D 211 1986 267 295
    • (1986) Physica D , vol.211 , pp. 267-295
    • Greene, J.M.1    MacKay, R.S.2    Stark, J.3
  • 44
    • 0007310585 scopus 로고    scopus 로고
    • Global dynamics and fast indicators
    • IOP-Publishing Bristol
    • C. Sim Global dynamics and fast indicators Global Analysis of Dynamical Systems 2001 IOP-Publishing Bristol 373 390
    • (2001) Global Analysis of Dynamical Systems , pp. 373-390
    • Sim, C.1
  • 45
    • 0346684381 scopus 로고    scopus 로고
    • Central stable/unstable manifolds and the destruction of KAM tori in the planar Hill problem
    • C. Sim, and T. Stuchi Central stable/unstable manifolds and the destruction of KAM tori in the planar Hill problem Physica D 140 2000 1 32
    • (2000) Physica D , vol.140 , pp. 1-32
    • Sim, C.1    Stuchi, T.2
  • 46
    • 79951511912 scopus 로고    scopus 로고
    • Complex analysis of the invariant manifolds close to a singularity
    • C. Sim, A. Vieiro, Complex analysis of the invariant manifolds close to a singularity, Work in Progress, 2010.
    • (2010) Work in Progress
    • C. Simó1
  • 48
    • 33644695016 scopus 로고    scopus 로고
    • Dynamics in One Complex Variable
    • third ed. Princeton University Press Princeton, NJ
    • J. Milnor Dynamics in One Complex Variable third ed. Annals of Mathematics Studies vol. 160 2006 Princeton University Press Princeton, NJ
    • (2006) Annals of Mathematics Studies , vol.160
    • Milnor, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.