메뉴 건너뛰기




Volumn 8, Issue 4, 2007, Pages 971-1005

Attractors for return maps near homoclinic tangencies of three-dimensional dissipative diffeomorphisms

Author keywords

Invariant curves; Lyapunov exponents; Strange attractors

Indexed keywords


EID: 37349060057     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2007.8.971     Document Type: Article
Times cited : (16)

References (25)
  • 2
    • 0001870459 scopus 로고
    • The dynamics of the Hénon map
    • M. Benedicks and L. Carleson, The dynamics of the Hénon map, Ann. Math., 133 (1991), 73-169.
    • (1991) Ann. Math , vol.133 , pp. 73-169
    • Benedicks, M.1    Carleson, L.2
  • 3
    • 0006963160 scopus 로고    scopus 로고
    • Towards global models near homoclinic tangencies of dissipative diffeomorphisms
    • H. Broer, C. Simó 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    Simó, C.2    Tatjer, J.C.3
  • 4
    • 0000709901 scopus 로고    scopus 로고
    • Infinitely many coexisting strange attractors
    • E. Colli, Infinitely many coexisting strange attractors, Ann. Inst. H. Poincaré, 15 (1998), 539-579.
    • (1998) Ann. Inst. H. Poincaré , vol.15 , pp. 539-579
    • Colli, E.1
  • 6
    • 0037445370 scopus 로고    scopus 로고
    • A route to computational chaos revisited: Noninvertibility and the breakup of an invariant circle
    • C. E. Frouzakis, I. G. Kevrekidis and B. B. Peckham, A route to computational chaos revisited: noninvertibility and the breakup of an invariant circle, Physica D, 177 (2003), 101-121.
    • (2003) Physica D , vol.177 , pp. 101-121
    • Frouzakis, C.E.1    Kevrekidis, I.G.2    Peckham, B.B.3
  • 7
    • 37349105501 scopus 로고    scopus 로고
    • Bifurcations of three-Dimensional diffeomorphisms with non-simple quadratic homoclinic tangencies and generalized Hénon maps
    • S. V. Gonchenko, V. S. Gonchenko and J. C. Tatjer, Bifurcations of three-Dimensional diffeomorphisms with non-simple quadratic homoclinic tangencies and generalized Hénon maps. Regular and Chaotic Dynamics, 12 (2007), 233-266.
    • (2007) Regular and Chaotic Dynamics , vol.12 , pp. 233-266
    • Gonchenko, S.V.1    Gonchenko, V.S.2    Tatjer, J.C.3
  • 8
    • 0002053804 scopus 로고
    • Absolutely continuous invariant measures for one parameter families of one-dimensional maps
    • M. Jacobson, Absolutely continuous invariant measures for one parameter families of one-dimensional maps, Commum. Math. Phys., 81 (1981), 39-88.
    • (1981) Commum. Math. Phys , vol.81 , pp. 39-88
    • Jacobson, M.1
  • 9
    • 0001640825 scopus 로고
    • Chaotic behavior of multidimensional difference equations
    • J. L. Kaplan and J. A. Yorke, Chaotic behavior of multidimensional difference equations, Lecture Notes in Mathematics, 730 (1979), 204-227.
    • (1979) Lecture Notes in Mathematics , vol.730 , pp. 204-227
    • Kaplan, J.L.1    Yorke, J.A.2
  • 11
    • 0000305898 scopus 로고
    • Computational chaos-a prelude to computational instability
    • E. N. Lorenz, Computational chaos-a prelude to computational instability, Physica D, 35 (1989), 299-317.
    • (1989) Physica D , vol.35 , pp. 299-317
    • Lorenz, E.N.1
  • 12
    • 34250112778 scopus 로고
    • On the concept of attractor
    • J. Milnor, On the concept of attractor, Commun. Math. Phys., 99 (1985), 177-195.
    • (1985) Commun. Math. Phys , vol.99 , pp. 177-195
    • Milnor, J.1
  • 14
    • 0242344635 scopus 로고
    • Abundance of strange attractors
    • L. Mora and M. Viana, Abundance of strange attractors, Acta Mathematica, 171 (1993), 1-71.
    • (1993) Acta Mathematica , vol.171 , pp. 1-71
    • Mora, L.1    Viana, M.2
  • 15
    • 32044475236 scopus 로고
    • Diffeomorphisms with infinitely many sinks
    • S. Newhouse, Diffeomorphisms with infinitely many sinks, Topology, 13 (1974), 9-18.
    • (1974) Topology , vol.13 , pp. 9-18
    • Newhouse, S.1
  • 17
    • 0039023464 scopus 로고
    • High dimension diffeomorphisms displaying infinitely many sinks
    • J. Palis and M. Viana, High dimension diffeomorphisms displaying infinitely many sinks, Ann. Math., 140 (1994), 91-136.
    • (1994) Ann. Math , vol.140 , pp. 91-136
    • Palis, J.1    Viana, M.2
  • 18
    • 0002862730 scopus 로고
    • Sur le problème des trois corps et les équations de la dynamique (Mem. couronné du prix de S.M. le roi Oscar II de Suède)
    • H. Poincaré, Sur le problème des trois corps et les équations de la dynamique (Mem. couronné du prix de S.M. le roi Oscar II de Suède). Acta Math., 13 (1890), 1-270.
    • (1890) Acta Math , vol.13 , pp. 1-270
    • Poincaré, H.1
  • 19
    • 0007390661 scopus 로고    scopus 로고
    • Coexistence and Persistence of Strange Attractors
    • Springer, New York
    • A. Pumariño and J. A. Rodriguez, "Coexistence and Persistence of Strange Attractors," Lecture Notes in Mathematics, 1658, Springer, New York, 1997.
    • (1997) Lecture Notes in Mathematics , vol.1658
    • Pumariño, A.1    Rodriguez, J.A.2
  • 20
    • 0035621941 scopus 로고    scopus 로고
    • Coexistence and persistence of infinitely many strange attractors
    • A. Pumariño and J. A. Rodríguez, Coexistence and persistence of infinitely many strange attractors, Ergodic Theory and Dynamical Systems, 21 (2001), 1511-1523.
    • (2001) Ergodic Theory and Dynamical Systems , vol.21 , pp. 1511-1523
    • Pumariño, A.1    Rodríguez, J.A.2
  • 21
    • 33846055493 scopus 로고    scopus 로고
    • Dynamics near homoclinic bifurcations of three-dimensional dissipative diffeomorphisms
    • A. Pumariño and J. C. Tatjer, Dynamics near homoclinic bifurcations of three-dimensional dissipative diffeomorphisms, Nonlinearity, 19 (2006), 2833-2852.
    • (2006) Nonlinearity , vol.19 , pp. 2833-2852
    • Pumariño, A.1    Tatjer, J.C.2
  • 24
    • 0035628941 scopus 로고    scopus 로고
    • Three-dimensional dissipative diffeomorphisms with homoclinic tangencies
    • J. C. Tatjer, Three-dimensional dissipative diffeomorphisms with homoclinic tangencies, Ergodic Theory and Dynamical Systems, 21 (2001), 249-302.
    • (2001) Ergodic Theory and Dynamical Systems , vol.21 , pp. 249-302
    • Tatjer, J.C.1
  • 25
    • 0001951104 scopus 로고
    • Strange attractors in higher dimensions
    • M. Viana, Strange attractors in higher dimensions, Bol. Soc. Bras. Mat., 24 (1993), 13-62.
    • (1993) Bol. Soc. Bras. Mat , vol.24 , pp. 13-62
    • Viana, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.