Computational Proofs in Dynamics
暂无分享,去创建一个
[1] P. Pilarczyk,et al. Global dynamics in a stage-structured discrete-time population model with harvesting. , 2012, Journal of theoretical biology.
[2] R. Canosa,et al. The parameterization method for invariant manifolds I: manifolds associated to non-resonant subspaces , 2002 .
[3] Konstantin Mischaikow,et al. Rigorous Computations of Homoclinic Tangencies , 2006, SIAM J. Appl. Dyn. Syst..
[4] Hans Koch,et al. Integration of Dissipative Partial Differential Equations: A Case Study , 2010, SIAM J. Appl. Dyn. Syst..
[5] James F. Selgrade,et al. A geometric criterion for hyperbolicity of flows , 1977 .
[6] Konstantin Mischaikow,et al. Rigorous Numerics for Global Dynamics: A Study of the Swift-Hohenberg Equation , 2005, SIAM J. Appl. Dyn. Syst..
[7] C. Conley. Isolated Invariant Sets and the Morse Index , 1978 .
[8] J. Eckmann,et al. A computer-assisted proof of universality for area-preserving maps , 1984 .
[9] Wolf-Jürgen Beyn,et al. The Numerical Computation of Homoclinic Orbits for Maps , 1997 .
[10] Robert E. Tarjan,et al. Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..
[11] O. Lanford. A computer-assisted proof of the Feigenbaum conjectures , 1982 .
[12] Pierre Collet,et al. Universal properties of maps on an interval , 1980 .
[13] J. Lessard. Recent advances about the uniqueness of the slowly oscillating periodic solutions of Wright's equation , 2009, 0909.4107.
[14] Robert W. Easton,et al. Isolating blocks and symbolic dynamics , 1975 .
[15] F. Dumortier,et al. Cocoon bifurcation in three-dimensional reversible vector fields , 2006 .
[16] Rafael de la Llave,et al. A parameterization method for the computation of invariant tori andtheir whiskers in quasi-periodic maps: Numerical algorithms , 2006 .
[17] J. Robbin,et al. Dynamical systems, shape theory and the Conley index , 1988, Ergodic Theory and Dynamical Systems.
[18] R. Llave,et al. KAM theory without action-angle variables , 2005 .
[19] H. Koçak,et al. Homoclinic Shadowing , 2005 .
[20] K. Mischaikow,et al. Chaos in the Lorenz equations: a computer-assisted proof , 1995, math/9501230.
[21] Michael Dellnitz,et al. Chapter 5 - Set Oriented Numerical Methods for Dynamical Systems , 2002 .
[22] George R. Sell,et al. Existence of dichotomies and invariant splittings for linear differential systems, II☆ , 1976 .
[23] Konstantin Mischaikow,et al. A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems , 2009, SIAM J. Appl. Dyn. Syst..
[24] S. S. Cairns,et al. Differential and combinatorial topology : a symposium in honor of Marston Morse , 1965 .
[25] R. de la Llave,et al. Accurate strategies for small divisor problems , 1990 .
[26] Piotr Zgliczynski,et al. Rigorous Numerics for Dissipative Partial Differential Equations II. Periodic Orbit for the Kuramoto–Sivashinsky PDE—A Computer-Assisted Proof , 2004, Found. Comput. Math..
[27] Rafael M. Frongillo,et al. Algorithms for Rigorous Entropy Bounds and Symbolic Dynamics , 2008, SIAM J. Appl. Dyn. Syst..
[28] Cone Conditions and Covering Relations for Topologically Normally Hyperbolic Invariant Manifolds , 2011, 1103.1959.
[29] Hüseyin Koçak,et al. Transversal connecting orbits from shadowing , 2007, Numerische Mathematik.
[30] Konstantin Mischaikow,et al. Rigorous Numerics for Symmetric Connecting Orbits: Even Homoclinics of the Gray-Scott Equation , 2011, SIAM J. Math. Anal..
[31] Konstantin Mischaikow,et al. A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems , 2004, SIAM J. Appl. Dyn. Syst..
[32] W. Tucker,et al. A Note on the Convergence of Parametrised Non-Resonant Invariant Manifolds , 2008, 0811.4500.
[33] Jean-Philippe Lessard,et al. Rigorous computation of smooth branches of equilibria for the three dimensional Cahn–Hilliard equation , 2011, Numerische Mathematik.
[34] Thomas Wanner,et al. Structure of the Attractor of the Cahn-hilliard equation on a Square , 2007, Int. J. Bifurc. Chaos.
[35] The stable manifold theorem via an isolating block , 1973 .
[36] W. Kyner. Invariant Manifolds , 1961 .
[37] Siegfried M. Rump,et al. Verification methods: rigorous results using floating-point arithmetic , 2010, Acta Numerica.
[38] Pathology in dynamical systems II: Applications , 1976 .
[39] Konstantin Mischaikow,et al. An Algorithmic Approach to Chain Recurrence , 2005, Found. Comput. Math..
[40] A. Neumaier,et al. Rigorous chaos verification in discrete dynamical systems , 1993 .
[41] Siegfried M. Rump,et al. INTLAB - INTerval LABoratory , 1998, SCAN.
[42] M. Feigenbaum. Quantitative universality for a class of nonlinear transformations , 1978 .
[43] Daniel Wilczak,et al. Heteroclinic Connections Between Periodic Orbits in Planar Restricted Circular Three Body Problem. Part II , 2004 .
[44] Jean-Philippe Lessard,et al. Chaotic Braided Solutions via Rigorous Numerics: Chaos in the Swift-Hohenberg Equation , 2008, SIAM J. Appl. Dyn. Syst..
[45] James A. Yorke,et al. Rigorous verification of trajectories for the computer simulation of dynamical systems , 1991 .
[46] H. Kokubu,et al. Rigorous verification of cocoon bifurcations in the Michelson system , 2007 .
[47] Gianni Arioli,et al. Computer-Assisted Methods for the Study of Stationary Solutions in Dissipative Systems, Applied to the Kuramoto–Sivashinski Equation , 2010 .
[48] Wolf-Jürgen Beyn,et al. The Numerical Computation of Connecting Orbits in Dynamical Systems , 1990 .
[49] C. Fefferman,et al. Relativistic Stability of Matter - I , 1986 .
[50] Clark Robinson,et al. Bifurcation to infinitely many sinks , 1983 .
[51] Daniel Stoffer,et al. Rigorous verification of chaotic behaviour of maps using validated shadowing , 1999 .
[52] Michael Plum,et al. Computer-assisted proofs for semilinear elliptic boundary value problems , 2009 .
[53] Konstantin Mischaikow,et al. Validated Continuation for Equilibria of PDEs , 2007, SIAM J. Numer. Anal..
[54] Kenneth J. Palmer,et al. Chaos in the Duffing Equation , 1993 .
[55] Marian Gidea,et al. Covering relations for multidimensional dynamical systems , 2004 .
[56] Zin Arai,et al. On Hyperbolic Plateaus of the Hénon Map , 2007, Exp. Math..
[57] Konstantin Mischaikow,et al. Graph Approach to the Computation of the Homology of Continuous Maps , 2005, Found. Comput. Math..
[58] Warwick Tucker,et al. Foundations of Computational Mathematics a Rigorous Ode Solver and Smale's 14th Problem , 2022 .
[59] M. Gameiro,et al. Topological Horseshoes of Traveling Waves for a Fast–Slow Predator–Prey System , 2007 .
[60] R. Canosa,et al. The parameterization method for invariant manifolds III: overview and applications , 2003 .
[61] Konstantin Mischaikow,et al. Global smooth solution curves using rigorous branch following , 2010, Math. Comput..
[62] D. Wilczak,et al. Heteroclinic Connections Between Periodic Orbits in Planar Restricted Circular Three-Body Problem – A Computer Assisted Proof , 2002, math/0201278.
[63] Martin Berz,et al. On the Estimation of Topological Entropy on Surfaces , 2008 .
[64] 中尾 充宏. Numerical Verification Methods for Solutions of Ordinary and Partial Differential Equations (数学解析の理論的展開の計算機上での遂行可能性) , 2000 .
[65] J. Eckmann,et al. Iterated maps on the interval as dynamical systems , 1980 .
[66] S. Pilyugin. Shadowing in dynamical systems , 1999 .
[67] Oscar E. Lanford,et al. Computer-assisted proofs in analysis , 1984 .
[68] S. Smale. Diffeomorphisms with Many Periodic Points , 1965 .
[69] Daniel Wilczak,et al. Uniformly Hyperbolic Attractor of the Smale-Williams Type for a Poincaré Map in the Kuznetsov System , 2010, SIAM J. Appl. Dyn. Syst..