메뉴 건너뛰기




Volumn 34, Issue 3, 1997, Pages 1207-1236

The numerical computation of homoclinic orbits for maps

Author keywords

Dynamical systems; Homoclinic points for maps; Numerical methods; Shadowing

Indexed keywords


EID: 0000997063     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142995281693     Document Type: Article
Times cited : (72)

References (25)
  • 1
    • 0001128796 scopus 로고
    • Numerical Continuation Methods: An Introduction
    • Springer. Berlin
    • E. L. ALLGOWER AND K. GEORG, Numerical Continuation Methods: An Introduction, Springer Ser. Comput. Math., 13. Springer. Berlin, 1990.
    • (1990) Springer Ser. Comput. Math. , vol.13
    • Allgower, E.L.1    Georg, K.2
  • 2
    • 0002433039 scopus 로고
    • Global bifurcations and their numerical computations
    • D. Roose, A. Spence. B. De Dier. eds., Kluwer Academic Publishers, Dordrecht
    • W. J. BEYN. Global bifurcations and their numerical computations, in Continuation and Bifurcation; Numerical Techniques and Applications, D. Roose, A. Spence. B. De Dier. eds., Kluwer Academic Publishers, Dordrecht, 1990, pp. 169-181.
    • (1990) Continuation and Bifurcation; Numerical Techniques and Applications , pp. 169-181
    • Beyn, W.J.1
  • 3
    • 0002836643 scopus 로고
    • The effect of discretization on homoclinic orbits
    • Bifurcation: Analysis, Algorithms, Applications, T. Küpper, R. Seydel, H. Troger, eds., Birkhäuser, Stuttgart
    • W. J. BEYN, The effect of discretization on homoclinic orbits, in Bifurcation: Analysis, Algorithms, Applications, T. Küpper, R. Seydel, H. Troger, eds., ISNM 79, Birkhäuser, Stuttgart, 1987, pp. 1-8.
    • (1987) ISNM , vol.79 , pp. 1-8
    • Beyn, W.J.1
  • 4
    • 0001340513 scopus 로고
    • The numerical computation of connecting orbits in dynamical systems
    • W. J. BEYN, The numerical computation of connecting orbits in dynamical systems, IMA J. Numer. Anal., 9 (1990), pp. 379-405.
    • (1990) IMA J. Numer. Anal. , vol.9 , pp. 379-405
    • Beyn, W.J.1
  • 5
    • 0001080429 scopus 로고
    • Dichotomies for linear difference equations
    • C. V. COFFMAN AND J. J. SCHÄFFER, Dichotomies for linear difference equations, Math. Ann., 172 (1967), pp. 139-166.
    • (1967) Math. Ann. , vol.172 , pp. 139-166
    • Coffman, C.V.1    Schäffer, J.J.2
  • 6
    • 0041581689 scopus 로고
    • Periodic shadowing
    • Chaotic Numerics, P. E. Kloeden, K. J. Palmer, eds., Amererican Mathematical Society, Providence, RI
    • B. A. COOMES, H. KOÇAK, AND K. J. PALMER, Periodic shadowing, in Chaotic Numerics, P. E. Kloeden, K. J. Palmer, eds., Contemp. Math. 172, Amererican Mathematical Society, Providence, RI, 1994, pp. 115-130.
    • (1994) Contemp. Math. , vol.172 , pp. 115-130
    • Coomes, B.A.1    Koçak, H.2    Palmer, K.J.3
  • 7
    • 0028479087 scopus 로고
    • Shadowing orbits of ordinary differential equations
    • B. A. COOMES, H. KOÇAK, AND K. J. PALMER, Shadowing orbits of ordinary differential equations, J. Comput. Appl. Math., 52 (1994), pp. 35-43.
    • (1994) J. Comput. Appl. Math. , vol.52 , pp. 35-43
    • Coomes, B.A.1    Koçak, H.2    Palmer, K.J.3
  • 9
    • 0001058067 scopus 로고
    • Numerical computation of heteroclinic orbits
    • E. J. DOEDEL AND M. J. FRIEDMAN. Numerical computation of heteroclinic orbits. J. Comput. Appl. Math.. 26 (1989), pp. 159-170.
    • (1989) J. Comput. Appl. Math.. , vol.26 , pp. 159-170
    • Doedel, E.J.1    Friedman, M.J.2
  • 10
    • 0029691221 scopus 로고    scopus 로고
    • Discretization of homoclinic orbits, rapid forcing and "invisible" chaos
    • B. FIEDLER AND J. SCHEURLE, Discretization of homoclinic orbits, rapid forcing and "invisible" chaos, Mem. Amer. Math. Soc., 570 (1996).
    • (1996) Mem. Amer. Math. Soc. , vol.570
    • Fiedler, B.1    Scheurle, J.2
  • 11
    • 0026170304 scopus 로고
    • Numerical computation of invariant manifolds connecting fixed pointa
    • M. J. FRIEDMAN AND E. J. DOEDEL, Numerical computation of invariant manifolds connecting fixed pointa, SIAM J. Numer. Anal., 28 (1991), pp. 789-808.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 789-808
    • Friedman, M.J.1    Doedel, E.J.2
  • 13
    • 0003235528 scopus 로고
    • Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields
    • Springer, New York
    • J. GUCKENHEIMER AND PH. HOLMES, Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields, Appl. Math. Sci. 42, Springer, New York, 1990.
    • (1990) Appl. Math. Sci. , vol.42
    • Guckenheimer, J.1    Holmes, P.H.2
  • 14
    • 0003275217 scopus 로고
    • Dynamics and Bifurcation
    • Springer, New York
    • J. HALE AND H. KOÇAK, Dynamics and Bifurcation, Texts Appl. Math. 3, Springer, New York, 1991.
    • (1991) Texts Appl. Math. , vol.3
    • Hale, J.1    Koçak, H.2
  • 15
    • 0003304963 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • Springer, Berlin
    • D. HENRY, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math, 840, Springer, Berlin, 1981.
    • (1981) Lecture Notes in Math , vol.840
    • Henry, D.1
  • 16
    • 0004171442 scopus 로고
    • Smooth Dynamical Systems
    • Academic Press, London
    • M. C. IRWIN, Smooth Dynamical Systems, Pure Appl. Math. 84, Academic Press, London, 1980.
    • (1980) Pure Appl. Math. , vol.84
    • Irwin, M.C.1
  • 19
    • 0001029040 scopus 로고
    • Rigorous chaos verification in discrete dynamical systems
    • A. NEUMAIER AND T. RAGE, Rigorous chaos verification in discrete dynamical systems, Phys. D, 67 (1993), pp. 327-346.
    • (1993) Phys. D , vol.67 , pp. 327-346
    • Neumaier, A.1    Rage, T.2
  • 21
    • 48549112859 scopus 로고
    • Exponential dichotomies and transversal homoclinic points
    • K. J. PALMER, Exponential dichotomies and transversal homoclinic points, J. Differential Equations, 55 (1984), pp. 225-256.
    • (1984) J. Differential Equations , vol.55 , pp. 225-256
    • Palmer, K.J.1
  • 22
    • 0001261668 scopus 로고
    • Exponential dichotomies, the shadowing lemma and transversal homoclinic points
    • U. Kirchgraber, H.-O. Walther, eds., Teubner, Stuttgart
    • K. J. PALMER, Exponential dichotomies, the shadowing lemma and transversal homoclinic points, in Dynamics Reported I, U. Kirchgraber, H.-O. Walther, eds., Teubner, Stuttgart, 1988, pp. 265-306.
    • (1988) Dynamics Reported , vol.1 , pp. 265-306
    • Palmer, K.J.1
  • 23
    • 0000063614 scopus 로고
    • On a Poincaré-Birkhoff problem
    • L. P. ŠIL'NIKOV, On a Poincaré-Birkhoff problem, Math. USSR-Sb., 3 (1967), pp. 353-371.
    • (1967) Math. USSR-Sb. , vol.3 , pp. 353-371
    • ŠiL'Nikov, L.P.1
  • 24
    • 84968514104 scopus 로고
    • Differentiable dynamical systems
    • S. SMALE, Differentiable dynamical systems, Bull. Amer. Math. Soc., 73 (1967). pp. 747-817.
    • (1967) Bull. Amer. Math. Soc. , vol.73 , pp. 747-817
    • Smale, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.