메뉴 건너뛰기




Volumn 194, Issue 2, 2003, Pages 433-459

Chaos in the Kuramoto-Sivashinsky equations - A computer-assisted proof

Author keywords

Covering relations; Differential equations; Dynamical systems; Rigorous numerical analysis; Symmetric periodic solutions

Indexed keywords


EID: 0142119428     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0396(03)00104-9     Document Type: Article
Times cited : (28)

References (18)
  • 1
    • 0035917024 scopus 로고    scopus 로고
    • Symbolic dynamics for the Hénon-Heiles Hamiltonian on the critical level
    • G. Arioli, P. Zgliczyński, Symbolic dynamics for the Hénon-Heiles Hamiltonian on the critical level, J. Differential Equations 171 (2001) 173-202.
    • (2001) J. Differential Equations , vol.171 , pp. 173-202
    • Arioli, G.1    Zgliczyński, P.2
  • 2
    • 85030965774 scopus 로고    scopus 로고
    • Computer Assisted Proofs in Dynamics Group
    • Computer Assisted Proofs in Dynamics Group, http://limba.ii.uj.edu.pl/~capd.
  • 3
    • 0004247206 scopus 로고
    • Lectures on Algebraic Topology
    • Springer, Berlin, Heidelberg, New York
    • A. Dold, Lectures on Algebraic Topology, Springer, Berlin, Heidelberg, New York, 1972.
    • (1972)
    • Dold, A.1
  • 4
    • 0142078250 scopus 로고
    • Wprowadzenie do topologii, PWN, Warszawa
    • R. Duda, Wprowadzenie do topologii, PWN, Warszawa, 1986.
    • (1986)
    • Duda, R.1
  • 5
    • 0003427204 scopus 로고
    • Reversing symmetries in dynamical systems
    • Ph.D. Thesis, Universiteit van Amsterdam
    • J.S.W. Lamb, Reversing symmetries in dynamical systems, Ph.D. Thesis, Universiteit van Amsterdam, 1994.
    • (1994)
    • Lamb, J.S.W.1
  • 6
    • 0002422258 scopus 로고
    • Computation of guaranted enclosures for solutions of ordinary initial and boundary value problems
    • J.R. Cash, I. Gladwell (Eds.), Clarendon Press, Oxford
    • R.J. Lohner, Computation of guaranted enclosures for solutions of ordinary initial and boundary value problems, in: J.R. Cash, I. Gladwell (Eds.), Computational Ordinary Differential Equations, Clarendon Press, Oxford, 1992.
    • (1992) Computational Ordinary Differential Equations
    • Lohner, R.J.1
  • 7
    • 25544449558 scopus 로고
    • Steady solutions of the Kuramoto-Sivashinsky equation
    • D. Michelson, Steady solutions of the Kuramoto-Sivashinsky equation, Physica D 19 (1986) 679.
    • (1986) Physica D , vol.19 , pp. 679
    • Michelson, D.1
  • 8
    • 0017552542 scopus 로고
    • Nonlinear analysis of hydrodynamic instability in laminar flames, II. Numerical experiments
    • D. Michelson, G. Sivashinsky, Nonlinear analysis of hydrodynamic instability in laminar flames, II. Numerical experiments, Acta Astronaut. 4 (1977) 1207-1221.
    • (1977) Acta Astronaut. , vol.4 , pp. 1207-1221
    • Michelson, D.1    Sivashinsky, G.2
  • 10
    • 67649370946 scopus 로고    scopus 로고
    • Conley Index
    • B. Fiedler (Ed.), Elsevier Science B.V. Chapter 9
    • K. Mischaikow, M. Mrozek, Conley Index, in: B. Fiedler (Ed.), Handbook of Dynamical Systems, Elsevier Science B.V. Vol. 2, Chapter 9, 2002, 393-460.
    • (2002) Handbook of Dynamical Systems , vol.2 , pp. 393-460
    • Mischaikow, K.1    Mrozek, M.2
  • 11
    • 0041690928 scopus 로고    scopus 로고
    • Heteroclinic connections in the Kuramoto-Sivashinsky equation: A computer assisted proof
    • M. Mrozek, M. Zelawski, Heteroclinic connections in the Kuramoto-Sivashinsky equation: a computer assisted proof, Reliable Comput. 3 (1997) 277-285.
    • (1997) Reliable Comput. , vol.3 , pp. 277-285
    • Mrozek, M.1    Zelawski, M.2
  • 12
    • 0012488396 scopus 로고    scopus 로고
    • Set arithmetic and the enclosing problem in dynamics
    • M. Mrozek, P. Zgliczyński, Set arithmetic and the enclosing problem in dynamics, Ann. Polon. Math. LXXIV (2000) 237-259.
    • (2000) Ann. Polon. Math. , vol.74 , pp. 237-259
    • Mrozek, M.1    Zgliczyński, P.2
  • 13
    • 38249026494 scopus 로고
    • The existence of steady solutions of the Kuramoto-Sivashinsky equation
    • W.C. Troy, The existence of steady solutions of the Kuramoto-Sivashinsky equation, J. Differential Equations 82 (1989) 269-313.
    • (1989) J. Differential Equations , vol.82 , pp. 269-313
    • Troy, W.C.1
  • 14
    • 85030963866 scopus 로고    scopus 로고
    • D. Wilczak, http://www.wsb-niu.edu.pl/~dwilczak.
    • Wilczak, D.1
  • 15
    • 0037346778 scopus 로고    scopus 로고
    • Heteroclinic connections between periodic orbits in planar restricted circular three body problem - A computer assisted proof
    • D. Wilczak, P. Zgliczyński, Heteroclinic connections between periodic orbits in planar restricted circular three body problem - a computer assisted proof, Commun. Math. Phys. 234 (2003) 37-75.
    • (2003) Commun. Math. Phys. , vol.234 , pp. 37-75
    • Wilczak, D.1    Zgliczyński, P.2
  • 16
    • 0000527735 scopus 로고    scopus 로고
    • Fixed points index for iteration of maps, topological horseshoe and chaos
    • P. Zgliczyński, Fixed points index for iteration of maps, topological horseshoe and chaos, Topological Methods in Nonlinear Analysis, Vol. 8, 1996, pp. 169-177.
    • (1996) Topological Methods in Nonlinear Analysis , vol.8 , pp. 169-177
    • Zgliczyński, P.1
  • 17
    • 0041540896 scopus 로고    scopus 로고
    • Computer assisted proof of chaos in the Rössler equations and the Hénon map
    • P. Zgliczyński, Computer assisted proof of chaos in the Rössler equations and the Hénon map, Nonlinearity 10 (1997) 243-252.
    • (1997) Nonlinearity , vol.10 , pp. 243-252
    • Zgliczyński, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.