메뉴 건너뛰기




Volumn 246, Issue 5, 2009, Pages 1774-1819

Covering relations, cone conditions and the stable manifold theorem

Author keywords

Cone condition; Covering relation; Hyperbolicity; Invariant manifold; Lyapunov function

Indexed keywords


EID: 58749090749     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2008.12.019     Document Type: Article
Times cited : (75)

References (39)
  • 1
    • 0036027227 scopus 로고    scopus 로고
    • Periodic orbits, symbolic dynamics and topological entropy for the restricted 3-body problem
    • Arioli G. Periodic orbits, symbolic dynamics and topological entropy for the restricted 3-body problem. Comm. Math. Phys. 231 1 (2002) 1-24
    • (2002) Comm. Math. Phys. , vol.231 , Issue.1 , pp. 1-24
    • Arioli, G.1
  • 2
    • 0035917024 scopus 로고    scopus 로고
    • Symbolic dynamics for the Hénon-Heiles Hamiltonian on the critical level
    • Arioli G., and Zgliczyński P. Symbolic dynamics for the Hénon-Heiles Hamiltonian on the critical level. J. Differential Equations 171 1 (2001) 173-202
    • (2001) J. Differential Equations , vol.171 , Issue.1 , pp. 173-202
    • Arioli, G.1    Zgliczyński, P.2
  • 3
    • 1042279871 scopus 로고    scopus 로고
    • Stable manifolds associated to fixed points with linear part equal to identity
    • Baldomá I., and Fontich E. Stable manifolds associated to fixed points with linear part equal to identity. J. Differential Equations 197 (2004) 45-72
    • (2004) J. Differential Equations , vol.197 , pp. 45-72
    • Baldomá, I.1    Fontich, E.2
  • 4
    • 9344233816 scopus 로고    scopus 로고
    • Stable manifolds and the Perron-Irwin method
    • Chaperon M. Stable manifolds and the Perron-Irwin method. Ergodic Theory Dynam. Systems 24 5 (2004) 1359-1394
    • (2004) Ergodic Theory Dynam. Systems , vol.24 , Issue.5 , pp. 1359-1394
    • Chaperon, M.1
  • 5
    • 33646882850 scopus 로고    scopus 로고
    • A verified optimization technique to locate chaotic regions of Hénon systems
    • Csendes T., Garay B., and Bánhelyi B. A verified optimization technique to locate chaotic regions of Hénon systems. J. Global Optim. 35 1 (2006) 145-160
    • (2006) J. Global Optim. , vol.35 , Issue.1 , pp. 145-160
    • Csendes, T.1    Garay, B.2    Bánhelyi, B.3
  • 6
    • 0002480739 scopus 로고
    • Isolating blocks and symbolic dynamics
    • Easton R. Isolating blocks and symbolic dynamics. J. Differential Equations 17 (1975) 96-118
    • (1975) J. Differential Equations , vol.17 , pp. 96-118
    • Easton, R.1
  • 7
    • 0001708795 scopus 로고
    • Homoclinic phenomena in Hamiltonian systems with several degrees of freedom
    • Easton R. Homoclinic phenomena in Hamiltonian systems with several degrees of freedom. J. Differential Equations 29 (1978) 241-252
    • (1978) J. Differential Equations , vol.29 , pp. 241-252
    • Easton, R.1
  • 8
    • 0033101751 scopus 로고    scopus 로고
    • Stable curves asymptotic to a degenerate fixed point
    • Fontich E. Stable curves asymptotic to a degenerate fixed point. Nonlinear Anal. 35 (1999) 711-733
    • (1999) Nonlinear Anal. , vol.35 , pp. 711-733
    • Fontich, E.1
  • 9
    • 0007431667 scopus 로고    scopus 로고
    • Rigorous numerical studies of the existence of periodic orbits for the Hénon map
    • SCAN'97. Lyon, 1997
    • Galias Z. Rigorous numerical studies of the existence of periodic orbits for the Hénon map. SCAN'97. Lyon, 1997. J.UCS 4 2 (1998) 114-124
    • (1998) J.UCS , vol.4 , Issue.2 , pp. 114-124
    • Galias, Z.1
  • 10
    • 0031063208 scopus 로고    scopus 로고
    • Positive topological entropy of Chua's circuit: A computer assisted proof
    • Galias Z. Positive topological entropy of Chua's circuit: A computer assisted proof. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 7 2 (1997) 331-349
    • (1997) Internat. J. Bifur. Chaos Appl. Sci. Engrg. , vol.7 , Issue.2 , pp. 331-349
    • Galias, Z.1
  • 11
    • 0001201892 scopus 로고    scopus 로고
    • Computer assisted proof of chaos in the Lorenz equations
    • Galias Z., and Zgliczyński P. Computer assisted proof of chaos in the Lorenz equations. Phys. D 115 3-4 (1998) 165-188
    • (1998) Phys. D , vol.115 , Issue.3-4 , pp. 165-188
    • Galias, Z.1    Zgliczyński, P.2
  • 12
    • 0035622331 scopus 로고    scopus 로고
    • Abundance of homoclinic and heteroclinic orbits and rigorous bounds for the topological entropy for the Hénon map
    • Galias Z., and Zgliczyński P. Abundance of homoclinic and heteroclinic orbits and rigorous bounds for the topological entropy for the Hénon map. Nonlinearity 14 5 (2001) 909-932
    • (2001) Nonlinearity , vol.14 , Issue.5 , pp. 909-932
    • Galias, Z.1    Zgliczyński, P.2
  • 13
    • 33644518721 scopus 로고    scopus 로고
    • Topological methods in the instability problem of Hamiltonian systems
    • Gidea M., and de la Llave R. Topological methods in the instability problem of Hamiltonian systems. Discrete Contin. Dyn. Syst. 14 2 (2006) 295-328
    • (2006) Discrete Contin. Dyn. Syst. , vol.14 , Issue.2 , pp. 295-328
    • Gidea, M.1    de la Llave, R.2
  • 14
    • 34249311964 scopus 로고    scopus 로고
    • Shadowing orbits for transition chains of invariant tori alternating with Birkhoff zones of instability
    • Gidea M., and Robinson C. Shadowing orbits for transition chains of invariant tori alternating with Birkhoff zones of instability. Nonlinearity 20 5 (2007) 1115-1143
    • (2007) Nonlinearity , vol.20 , Issue.5 , pp. 1115-1143
    • Gidea, M.1    Robinson, C.2
  • 15
    • 3543092733 scopus 로고    scopus 로고
    • Covering relations for multidimensional dynamical systems
    • Gidea M., and Zgliczyński P. Covering relations for multidimensional dynamical systems. J. Differential Equations 202 1 (2004) 33-58
    • (2004) J. Differential Equations , vol.202 , Issue.1 , pp. 33-58
    • Gidea, M.1    Zgliczyński, P.2
  • 19
    • 22944480883 scopus 로고    scopus 로고
    • A new proof of the stable manifold theorem for hyperbolic fixed points on surfaces
    • Holland M., and Luzzatto S. A new proof of the stable manifold theorem for hyperbolic fixed points on surfaces. J. Difference Equ. Appl. 11 6 (2005) 535-551
    • (2005) J. Difference Equ. Appl. , vol.11 , Issue.6 , pp. 535-551
    • Holland, M.1    Luzzatto, S.2
  • 20
    • 0010055859 scopus 로고
    • On the stable manifold theorem
    • Irwin M.C. On the stable manifold theorem. Bull. London Math. Soc. 2 (1970) 196-198
    • (1970) Bull. London Math. Soc. , vol.2 , pp. 196-198
    • Irwin, M.C.1
  • 21
    • 0001595986 scopus 로고
    • A new proof of the pseudostable manifold theorem
    • Irwin M.C. A new proof of the pseudostable manifold theorem. J. London Math. Soc. 21 (1980) 557-566
    • (1980) J. London Math. Soc. , vol.21 , pp. 557-566
    • Irwin, M.C.1
  • 22
    • 58749107817 scopus 로고    scopus 로고
    • Rigorous verification of the existence of cocoon bifurcation for the Michelson system
    • Kokubu H., Wilczak D., and Zgliczyński P. Rigorous verification of the existence of cocoon bifurcation for the Michelson system. Nonlinearity 20 (2007) 2147-2174
    • (2007) Nonlinearity , vol.20 , pp. 2147-2174
    • Kokubu, H.1    Wilczak, D.2    Zgliczyński, P.3
  • 23
    • 0002007686 scopus 로고
    • A stable manifold theorem for degenerate fixed points with applications to celestial mechanics
    • McGehee R. A stable manifold theorem for degenerate fixed points with applications to celestial mechanics. J. Differential Equations 14 (1973) 70-88
    • (1973) J. Differential Equations , vol.14 , pp. 70-88
    • McGehee, R.1
  • 24
    • 0030490229 scopus 로고    scopus 로고
    • A new proof of the stable manifold theorem
    • McGehee R., and Sander E. A new proof of the stable manifold theorem. Z. Angew. Math. Phys. 47 4 (1996) 497-513
    • (1996) Z. Angew. Math. Phys. , vol.47 , Issue.4 , pp. 497-513
    • McGehee, R.1    Sander, E.2
  • 25
    • 0035324902 scopus 로고    scopus 로고
    • Topological entropy for multidimensional perturbations of one-dimensional maps
    • Misiurewicz M., and Zgliczyński P. Topological entropy for multidimensional perturbations of one-dimensional maps. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 11 5 (2001) 1443-1446
    • (2001) Internat. J. Bifur. Chaos Appl. Sci. Engrg. , vol.11 , Issue.5 , pp. 1443-1446
    • Misiurewicz, M.1    Zgliczyński, P.2
  • 27
    • 0001029040 scopus 로고
    • Rigorous chaos verification in discrete dynamical system
    • Neumaier A., and Rage T. Rigorous chaos verification in discrete dynamical system. Phys. D 67 (1993) 327-346
    • (1993) Phys. D , vol.67 , pp. 327-346
    • Neumaier, A.1    Rage, T.2
  • 28
    • 12244303214 scopus 로고
    • Computation of the local stable and unstable manifolds
    • Ombach J. Computation of the local stable and unstable manifolds. Univ. Iagel. Acta Math. 32 (1995) 129-136
    • (1995) Univ. Iagel. Acta Math. , vol.32 , pp. 129-136
    • Ombach, J.1
  • 29
    • 0000561907 scopus 로고
    • Rigorous verification of chaos in a molecular model
    • Rage T., Neumaier A., and Schlier C. Rigorous verification of chaos in a molecular model. Phys. Rev. E 50 (1994) 2682-2688
    • (1994) Phys. Rev. E , vol.50 , pp. 2682-2688
    • Rage, T.1    Neumaier, A.2    Schlier, C.3
  • 30
    • 84972510836 scopus 로고
    • Stable manifolds of semi-hyperbolic fixed points
    • Robbin J.W. Stable manifolds of semi-hyperbolic fixed points. Illinois J. Math. 15 (1971) 595-609
    • (1971) Illinois J. Math. , vol.15 , pp. 595-609
    • Robbin, J.W.1
  • 32
    • 0002061016 scopus 로고    scopus 로고
    • A rigorous ODE solver and Smale's 14th problem
    • Tucker W. A rigorous ODE solver and Smale's 14th problem. Found. Comput. Math. 2 1 (2002) 53-117
    • (2002) Found. Comput. Math. , vol.2 , Issue.1 , pp. 53-117
    • Tucker, W.1
  • 33
    • 30644464142 scopus 로고    scopus 로고
    • Symmetric heteroclinic connections in the Michelson system-A computer assisted proof
    • Wilczak D. Symmetric heteroclinic connections in the Michelson system-A computer assisted proof. SIAM J. Appl. Dyn. Syst. 4 3 (2005) 489-514
    • (2005) SIAM J. Appl. Dyn. Syst. , vol.4 , Issue.3 , pp. 489-514
    • Wilczak, D.1
  • 34
    • 33846933597 scopus 로고    scopus 로고
    • The existence of Shilnikov homoclinic orbits in the Michelson system: A computer assisted proof
    • Wilczak D. The existence of Shilnikov homoclinic orbits in the Michelson system: A computer assisted proof. Found. Comput. Math. 6 (2006) 495-535
    • (2006) Found. Comput. Math. , vol.6 , pp. 495-535
    • Wilczak, D.1
  • 35
    • 0037346778 scopus 로고    scopus 로고
    • Heteroclinic connections between periodic orbits in planar restricted circular three-body problem-A computer assisted proof
    • Wilczak D., and Zgliczyński P. Heteroclinic connections between periodic orbits in planar restricted circular three-body problem-A computer assisted proof. Comm. Math. Phys. 234 1 (2003) 37-75
    • (2003) Comm. Math. Phys. , vol.234 , Issue.1 , pp. 37-75
    • Wilczak, D.1    Zgliczyński, P.2
  • 36
    • 34247254380 scopus 로고    scopus 로고
    • Topological method for symmetric periodic orbits for maps with a reversing symmetry
    • Wilczak D., and Zgliczyński P. Topological method for symmetric periodic orbits for maps with a reversing symmetry. Discrete Contin. Dyn. Sys. Ser. A 17 (2007) 629-652
    • (2007) Discrete Contin. Dyn. Sys. Ser. A , vol.17 , pp. 629-652
    • Wilczak, D.1    Zgliczyński, P.2
  • 37
    • 18144406872 scopus 로고    scopus 로고
    • Topological horseshoes and delay differential equations
    • Wójcik K., and Zgliczyński P. Topological horseshoes and delay differential equations. Discrete Contin. Dyn. Syst. 12 5 (2005) 827-852
    • (2005) Discrete Contin. Dyn. Syst. , vol.12 , Issue.5 , pp. 827-852
    • Wójcik, K.1    Zgliczyński, P.2
  • 38
    • 0041540896 scopus 로고    scopus 로고
    • Computer assisted proof of chaos in the Rössler equations and in the Hénon map
    • Zgliczyński P. Computer assisted proof of chaos in the Rössler equations and in the Hénon map. Nonlinearity 10 1 (1997) 243-252
    • (1997) Nonlinearity , vol.10 , Issue.1 , pp. 243-252
    • Zgliczyński, P.1
  • 39
    • 0033264634 scopus 로고    scopus 로고
    • Sharkovskii's theorem for multidimensional perturbations of one-dimensional maps
    • Zgliczyński P. Sharkovskii's theorem for multidimensional perturbations of one-dimensional maps. Ergodic Theory Dynam. Systems 19 6 (1999) 1655-1684
    • (1999) Ergodic Theory Dynam. Systems , vol.19 , Issue.6 , pp. 1655-1684
    • Zgliczyński, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.