Visual explorations of dynamics: The standard map
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[1] Michael Frazier,et al. Studies in Advanced Mathematics , 2004 .
[2] H. Poincaré,et al. Les méthodes nouvelles de la mécanique céleste , 1899 .
[3] S. Smale,et al. Finding a horseshoe on the beaches of Rio , 1998 .
[4] John M. Greene,et al. A method for determining a stochastic transition , 1979, Hamiltonian Dynamical Systems.
[5] Rafael de la Llave,et al. A Tutorial on Kam Theory , 2003 .
[6] Charles F. F. Karney. Long-time correlations in the stochastic regime , 1983, nlin/0501023.
[7] R. MacKay,et al. Linear Stability of Periodic Orbits in Lagrangian Systems , 1983, Hamiltonian Dynamical Systems.
[8] J. Bialek,et al. Fractal Diagrams for Hamiltonian Stochasticity , 1982, Hamiltonian Dynamical Systems.
[9] J. Pöschel,et al. A lecture on the classical KAM theorem , 2009, 0908.2234.
[10] A. Lichtenberg,et al. Regular and Chaotic Dynamics , 1992 .
[11] R. Llave,et al. Smooth Ergodic Theory and Its Applications , 2001 .
[12] R. MacKay. Greene's residue criterion , 1992 .
[13] B. Chirikov. A universal instability of many-dimensional oscillator systems , 1979 .
[14] J. M. Greene. THE CALCULATION OF KAM SURFACES * , 1980 .
[15] James D. Meiss,et al. Differential dynamical systems , 2007, Mathematical modeling and computation.
[16] V. Gelfreich,et al. Splitting of separatrices: perturbation theory and exponential smallness , 2001 .
[17] Rafael de la Llave,et al. KAM Theory and a Partial Justification of Greene's Criterion for Nontwist Maps , 2000, SIAM J. Math. Anal..
[18] Henri Poincaré,et al. méthodes nouvelles de la mécanique céleste , 1892 .
[19] I. Hargittai,et al. The mathematical intelligencer , 2008 .
[20] Robert S. MacKay,et al. Renormalisation in Area-Preserving Maps , 1993 .
[21] Seng Hu. A Variational Principle Associated to Positive Tilt Maps , 1998 .
[22] I. Percival,et al. Critical function and modular smoothing , 1990 .
[23] James D. Meiss,et al. Transport in Hamiltonian systems , 1984 .
[24] Characterization of fat fractals in nonlinear dynamical systems. , 1986, Physical review letters.
[25] J. Meiss. Symplectic maps, variational principles, and transport , 1992 .
[26] D. Chillingworth. DYNAMICAL SYSTEMS: STABILITY, SYMBOLIC DYNAMICS AND CHAOS , 1998 .
[27] J. Stark,et al. Locally most robust circles and boundary circles for area-preserving maps , 1992 .
[28] Robert W. Easton,et al. Geometric methods for discrete dynamical systems , 1998 .
[29] Dana D. Hobson,et al. An efficient method for computing invariant manifolds of planar maps , 1993 .
[30] James D. Meiss,et al. Algebraic decay in self-similar Markov chains , 1985 .
[31] P. Boyland. Rotation sets and Morse decompositions in twist maps , 1988, Ergodic Theory and Dynamical Systems.
[32] J. Meiss. Transient measures in the standard map , 1994 .
[33] J. Mather. Variational construction of orbits of twist diffeomorphisms , 1991 .
[34] S. Aubry. The twist map, the extended Frenkel-Kontorova model and the devil's staircase , 1983 .
[35] V. F. Lazutkin,et al. Splitting of separatrices for standard and semistandard mappings , 1989 .
[36] M. Feigenbaum,et al. Universal Behaviour in Families of Area-Preserving Maps , 1981, Hamiltonian Dynamical Systems.
[37] A. Veselov,et al. What Is an Integrable Mapping , 1991 .
[38] A. Apte,et al. Meanders and reconnection-collision sequences in the standard nontwist map. , 2004, Chaos.
[39] J. Lamb,et al. Time-reversal symmetry in dynamical systems: a survey , 1998 .
[40] Y. Suris,et al. Integrable mappings of the standard type , 1989 .
[41] A. Veselov,et al. New integrable deformations of the Calogero-Moser quantum problem , 1996 .
[42] Christophe Golé. Symplectic Twist Maps: Global Variational Techniques , 2001 .
[43] A. Andrianov. Composition of solutions of quadratic Diophantine equations , 1991 .
[44] S. Croucher,et al. Surveys , 1965, Understanding Communication Research Methods.
[45] R. MacKay. Equivariant universality classes , 1984 .
[46] James D. Meiss,et al. Heteroclinic orbits and Flux in a perturbed integrable Suris map , 1996, math/9604231.
[47] J. M. Greene. Two‐Dimensional Measure‐Preserving Mappings , 1968 .
[48] J. Mather,et al. Existence of quasi-periodic orbits for twist homeomorphisms of the annulus , 1982 .