메뉴 건너뛰기




Volumn 59, Issue 1-2, 2004, Pages 121-132

Hyperbolic trajectories of time discretizations

Author keywords

Exponential dichotomy; Hyperbolicity; Long time approximation; Numerical dynamics; Shadowing; Time discretization

Indexed keywords

CHAOS THEORY; COMPUTER SIMULATION; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

EID: 4544272717     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.07.005     Document Type: Article
Times cited : (3)

References (36)
  • 1
    • 34250725682 scopus 로고    scopus 로고
    • Differential geometry of webs
    • F.J.E. Dillen L.C.A. Verstraelen North-Holland Amsterdam
    • M.A. Akivis, and V.V. Goldberg Differential geometry of webs F.J.E. Dillen L.C.A. Verstraelen Handbook of Differential Geometry vol. 1 2000 North-Holland Amsterdam 1 152
    • (2000) Handbook of Differential Geometry , vol.1 , pp. 1-152
    • Akivis, M.A.1    Goldberg, V.V.2
  • 2
    • 0001500810 scopus 로고
    • On invariant closed curves for one-step methods
    • W.-J. Beyn On invariant closed curves for one-step methods Numer. Math. 51 1987 103 122
    • (1987) Numer. Math. , vol.51 , pp. 103-122
    • Beyn, W.-J.1
  • 4
    • 4544306616 scopus 로고    scopus 로고
    • Numerical approximation of normally hyperbolic invariant manifolds
    • H.W. Broer, A. Hagen, and G. Vegter Numerical approximation of normally hyperbolic invariant manifolds Discrete Contin. Dyn. Systems B, supplemental volume 2003 133 140
    • (2003) Discrete Contin. Dyn. Systems B , vol.SUPPL. VOLUME , pp. 133-140
    • Broer, H.W.1    Hagen, A.2    Vegter, G.3
  • 7
    • 33646888362 scopus 로고
    • Rigorous computational shadowing of orbits of ordinary differential equations
    • B.A. Coomes, H. Kocak, and K.J. Palmer Rigorous computational shadowing of orbits of ordinary differential equations Numer. Math. 69 1995 401 421
    • (1995) Numer. Math. , vol.69 , pp. 401-421
    • Coomes, B.A.1    Kocak, H.2    Palmer, K.J.3
  • 8
    • 0038279667 scopus 로고
    • A shadowing theorem for ordinary differential equations
    • B.A. Coomes, H. Kocak, and K.J. Palmer A shadowing theorem for ordinary differential equations Z. Angew. Math. Phys. 46 1995 85 106
    • (1995) Z. Angew. Math. Phys. , vol.46 , pp. 85-106
    • Coomes, B.A.1    Kocak, H.2    Palmer, K.J.3
  • 11
    • 0000223905 scopus 로고    scopus 로고
    • On the computation of Lyapunov exponents for continuous dynamical systems
    • L. Dieci, R.D. Russel, and E. Van Vleck On the computation of Lyapunov exponents for continuous dynamical systems SIAM J. Numer. Anal. 34 1997 402 423
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 402-423
    • Dieci, L.1    Russel, R.D.2    Van Vleck, E.3
  • 12
    • 0001356311 scopus 로고
    • Persistence and smoothness of invariant manifolds for flows
    • N. Fenichel Persistence and smoothness of invariant manifolds for flows Indiana Univ. Math. J. 21 1971 193 226
    • (1971) Indiana Univ. Math. J. , vol.21 , pp. 193-226
    • Fenichel, N.1
  • 19
    • 84968480383 scopus 로고
    • Numerical orbits of chaotic processes represent true orbits
    • S.M. Hammel, J.A. Yorke, and C. Grebogi Numerical orbits of chaotic processes represent true orbits Bull. Am. Math. Soc. 19 1988 465 469
    • (1988) Bull. Am. Math. Soc. , vol.19 , pp. 465-469
    • Hammel, S.M.1    Yorke, J.A.2    Grebogi, C.3
  • 22
    • 0001389356 scopus 로고
    • On the computation of invariant manifolds of fixed points
    • A.J. Homburg, H.M. Osinga, and G. Vegter On the computation of invariant manifolds of fixed points Z. Angew. Math. Phys. 46 1995 171 187
    • (1995) Z. Angew. Math. Phys. , vol.46 , pp. 171-187
    • Homburg, A.J.1    Osinga, H.M.2    Vegter, G.3
  • 23
    • 0011660230 scopus 로고
    • Spurious solutions of numerical methods for initial value problems
    • A. Humphries Spurious solutions of numerical methods for initial value problems IMA J. Numer. Math. 13 1993 263 290
    • (1993) IMA J. Numer. Math. , vol.13 , pp. 263-290
    • Humphries, A.1
  • 24
    • 0000649975 scopus 로고
    • Stable attracting sets in dynamical systems and in their one-step discretizations
    • P.E. Kloeden, and J. Lorenz Stable attracting sets in dynamical systems and in their one-step discretizations SIAM J. Numer. Anal. 23 1986 986 995
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 986-995
    • Kloeden, P.E.1    Lorenz, J.2
  • 25
  • 27
    • 0001261668 scopus 로고
    • Exponential dichotomies, the shadowing lemma and transversal homoclinic points
    • K. Palmer Exponential dichotomies, the shadowing lemma and transversal homoclinic points Dyn. Report. Expositions Dyn. Systems 1 1988 265 305
    • (1988) Dyn. Report. Expositions Dyn. Systems , vol.1 , pp. 265-305
    • Palmer, K.1
  • 29
    • 49349126301 scopus 로고
    • A spectral theory for linear differential systems
    • J. Sacker, and G.R. Sell A spectral theory for linear differential systems J. Differential Equations 27 1978 320 358
    • (1978) J. Differential Equations , vol.27 , pp. 320-358
    • Sacker, J.1    Sell, G.R.2
  • 30
    • 0038976122 scopus 로고
    • Runge-Kutta schemes for Hamiltonian systems
    • J.M. Sanz-Serna Runge-Kutta schemes for Hamiltonian systems BIT 28 1988 877 883
    • (1988) BIT , vol.28 , pp. 877-883
    • Sanz-Serna, J.M.1
  • 31
    • 0037643058 scopus 로고
    • Numerical ordinary differential equations vs. dynamical systems
    • D.S. Broomhead A. Iserles Clarendon Press Oxford
    • J.M. Sanz-Serna Numerical ordinary differential equations vs. dynamical systems D.S. Broomhead A. Iserles The Dynamics of Numerics and the Numerics of Dynamics 1992 Clarendon Press Oxford 81 106
    • (1992) The Dynamics of Numerics and the Numerics of Dynamics , pp. 81-106
    • Sanz-Serna, J.M.1
  • 32
    • 0000920052 scopus 로고
    • Rigorous verification of trajectories for computer simulations of dynamical systems
    • T. Sauer, and J.A. Yorke Rigorous verification of trajectories for computer simulations of dynamical systems Nonlinearity 4 1991 961 979
    • (1991) Nonlinearity , vol.4 , pp. 961-979
    • Sauer, T.1    Yorke, J.A.2
  • 33
    • 23044478284 scopus 로고
    • Exponential dichotomy for solutions of discrete systems
    • V.E. Slyusarchuk Exponential dichotomy for solutions of discrete systems translated from Ukrain. Mat. Zh. 35 1983 109 115
    • (1983) Translated from Ukrain. Mat. Zh. , vol.35 , pp. 109-115
    • Slyusarchuk, V.E.1
  • 36
    • 0011538645 scopus 로고
    • Un Critere pour l'approximation des solutions periodiques des equations de Navier-Stokes
    • E. Titi Un Critere pour l'approximation des solutions periodiques des equations de Navier-Stokes Analyse Math. 312 1991 41 43
    • (1991) Analyse Math. , vol.312 , pp. 41-43
    • Titi, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.