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Volumn 16, Issue 2, 2007, Pages 181-188

On hyperbolic plateaus of the hénon map

Author keywords

Computer assisted proof; H non map; Uniform hyperbolicity

Indexed keywords


EID: 34548332507     PISSN: 10586458     EISSN: 1944950X     Source Type: Journal    
DOI: 10.1080/10586458.2007.10128992     Document Type: Article
Times cited : (35)

References (23)
  • 2
    • 34047234612 scopus 로고    scopus 로고
    • Rigorous Computations of Homoclinic Tangencies
    • Z. Arai and K. Mischaikow. “Rigorous Computations of Homoclinic Tangencies.” SIAM J. Appl. Dyn. Syst. 5 (2006), 280–292.
    • (2006) SIAM J. Appl. Dyn. Syst. , vol.5 , pp. 280-292
    • Arai, Z.1    Mischaikow, K.2
  • 3
    • 34249928777 scopus 로고
    • 2: Currents, Equilibrium Measure and Hyperbolicity
    • 2: Currents, Equilibrium Measure and Hyperbolicity.” Invent. math. 103 (1991), 69–99.
    • (1991) Invent. Math. , vol.103 , pp. 69-99
    • Bedford, E.1    Smillie, J.2
  • 4
    • 15744371234 scopus 로고    scopus 로고
    • Real Polynomial Diffeomorphisms with Maximal Entropy: Tangencies
    • E. Bedford and J. Smillie. “Real Polynomial Diffeomorphisms with Maximal Entropy: Tangencies.” Ann. Math. 160 (2004), 1–26.
    • (2004) Ann. Math. , vol.160 , pp. 1-26
    • Bedford, E.1    Smillie, J.2
  • 6
    • 34548310661 scopus 로고    scopus 로고
    • The Hénon Family: The Complex Horseshoe Locus and Real Parameter Values
    • E. Bedford and J. Smillie. “The Hénon Family: The Complex Horseshoe Locus and Real Parameter Values.” Contemp. Math. 396 (2006), 21–36.
    • (2006) Contemp. Math. , vol.396 , pp. 21-36
    • Bedford, E.1    Smillie, J.2
  • 8
  • 9
    • 44949275020 scopus 로고
    • Markov Shifts in the Hénon Family
    • M. J. Davis, R. S. MacKay, and A. Sannami. “Markov Shifts in the Hénon Family.” Physica D, 52 (1991), 171–178.
    • (1991) Physica D , vol.52 , pp. 171-178
    • Davis, M.J.1    Mackay, R.S.2    Sannami, A.3
  • 10
    • 67649382019 scopus 로고    scopus 로고
    • Set Oriented Numerical Methods for Dynamical Systems
    • Amsterdam: North-Holland
    • M. Dellnitz and O. Junge. “Set Oriented Numerical Methods for Dynamical Systems.” In Handbook of Dynamical Systems II, pp. 221–264. Amsterdam: North-Holland, 2002.
    • (2002) Handbook of Dynamical Systems II , pp. 221-264
    • Dellnitz, M.1    Junge, O.2
  • 11
    • 0000671077 scopus 로고
    • Shift Automorphisms in the Hénon Mapping
    • R. Devaney and Z. Nitecki. “Shift Automorphisms in the Hénon Mapping.” Commun. Math. Phys. 67 (1979), 137–146.
    • (1979) Commun. Math. Phys. , vol.67 , pp. 137-146
    • Devaney, R.1    Nitecki, Z.2
  • 12
    • 8744313983 scopus 로고    scopus 로고
    • An Algorithm to Prune the Area-Preserving Hénon Map
    • R. Hagiwara and A. Shudo. “An Algorithm to Prune the Area-Preserving Hénon Map.” J. Phys. A: Math. Gen. 37 (2004), 10521–10543.
    • (2004) J. Phys. A: Math. Gen. , vol.37 , pp. 10521-10543
    • Hagiwara, R.1    Shudo, A.2
  • 13
    • 0004840008 scopus 로고
    • Lien entre les propriétés dun endomorphisme de dimension un et celles d’un difféomorphisme de dimension deux
    • H. El Hamouly and C. Mira. “Lien entre les propriétés d’un endomorphisme de dimension un et celles d’un difféomorphisme de dimension deux.” C. R. Acad. Sci. Paris Sér. I Math. 293 (1981), 525–528.
    • (1981) C. R. Acad. Sci. Paris Sér. I Math. , vol.293 , pp. 525-528
    • El Hamouly, H.1    Mira, C.2
  • 14
    • 33846858196 scopus 로고    scopus 로고
    • A Numerical Method for Constructing the Hyperbolic Structure of Complex H´enon Mappings
    • S. L. Hruska. “A Numerical Method for Constructing the Hyperbolic Structure of Complex H´enon Mappings.” Foundations of Computational Mathematics 6 (2006), 427–455.
    • (2006) Foundations of Computational Mathematics , vol.6 , pp. 427-455
    • Hruska, S.L.1
  • 15
    • 34548359646 scopus 로고    scopus 로고
    • Rigorous Numerical Studies of the Dynamics of Polynomial Skew Products of C2
    • S. L. Hruska. “Rigorous Numerical Studies of the Dynamics of Polynomial Skew Products of C2.” Contemp. Math. 396 (2006), 85–100.
    • (2006) Contemp. Math. , vol.396 , pp. 85-100
    • Hruska, S.L.1
  • 16
  • 17
    • 0004043484 scopus 로고    scopus 로고
    • Stability, Symbolic Dynamics, and Chaos, second edition. Boca Raton: CRC Press
    • C. Robinson. Dynamical Systems; Stability, Symbolic Dynamics, and Chaos, second edition. Boca Raton: CRC Press, 1999.
    • (1999) Dynamical Systems
    • Robinson, C.1
  • 18
    • 0001624408 scopus 로고
    • Existence of Dichotomies and Invariant Splitting for Linear Differential Systems I
    • R. J. Sacker and G. R. Sell. “Existence of Dichotomies and Invariant Splitting for Linear Differential Systems I.” J. Differential Equations 27 (1974), 429–458.
    • (1974) J. Differential Equations , vol.27 , pp. 429-458
    • Sacker, R.J.1    Sell, G.R.2
  • 19
    • 33645179457 scopus 로고
    • A Topological Classification of the Periodic Orbits of the H´enon Family
    • A. Sannami. “A Topological Classification of the Periodic Orbits of the H´enon Family.” Japan J. Appl. Math. 6 (1989), 291–300.
    • (1989) Japan J. Appl. Math. , vol.6 , pp. 291-300
    • Sannami, A.1
  • 20
    • 34548298222 scopus 로고
    • On the Structure of the Parameter Space of the Hénon Map
    • Amsterdam: Elsevier
    • A. Sannami. “On the Structure of the Parameter Space of the Hénon Map.” In Towards the Harnessing of Chaos, pp. 289–303. Amsterdam: Elsevier, 1994.
    • (1994) Towards the Harnessing of Chaos , pp. 289-303
    • Sannami, A.1
  • 21
    • 0004112038 scopus 로고
    • Reading, MA: Addison-Wesley
    • R. Sedgewick. Algorithms. Reading, MA: Addison-Wesley, 1983.
    • (1983) Algorithms
    • Sedgewick, R.1
  • 22
    • 0348225591 scopus 로고    scopus 로고
    • Homoclinic Bifurcations for the Hénon Map
    • D. Sterling, H. R. Dullin, and J. D. Meiss. “Homoclinic Bifurcations for the Hénon Map.” Physica D 134 (1999), 153–184.
    • (1999) Physica D , vol.134 , pp. 153-184
    • Sterling, D.1    Dullin, H.R.2    Meiss, J.D.3
  • 23
    • 21944433587 scopus 로고    scopus 로고
    • A Combinatorial Procedure for Finding Isolating Neighbourhoods and Index Pairs
    • A. Szymczak. “A Combinatorial Procedure for Finding Isolating Neighbourhoods and Index Pairs.” Proc. Roy. Soc. Edinburgh Sect. A 127 (1997), 1075–1088.
    • (1997) Proc. Roy. Soc. Edinburgh Sect. A , vol.127 , pp. 1075-1088
    • Szymczak, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.