Homoclinic orbits with many loops near a $0^2 i\omega$ resonant fixed point of Hamiltonian systems
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Eric Lombardi | Patrick Bernard | Tiphaine Jézéquel | P. Bernard | Eric Lombardi | Tiphaine Jézéquel
[1] Stig Larsson,et al. A Trigonometric Method for the Linear Stochastic Wave Equation , 2012, SIAM J. Numer. Anal..
[2] Clodoaldo Grotta Ragazzo,et al. On the Stability of Double Homoclinic Loops , 1997 .
[3] G. Lord,et al. Stochastic exponential integrators for finite element discretization of SPDEs for multiplicative and additive noise , 2011, 1103.1986.
[4] A. D. Bouard,et al. Weak and Strong Order of Convergence of a Semidiscrete Scheme for the Stochastic Nonlinear Schrodinger Equation , 2006 .
[5] G. Iooss,et al. Perturbed Homoclinic Solutions in Reversible 1:1 Resonance Vector Fields , 1993 .
[6] P. Kloeden,et al. Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space–time noise , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[7] M. Haragus,et al. Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems , 2010 .
[8] Arnulf Jentzen,et al. Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients , 2014, The Annals of Applied Probability.
[9] Klaus Kirchgässner,et al. Water waves for small surface tension: an approach via normal form , 1992, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.
[10] Klaus Kirchgässner,et al. Travelling Waves in a Chain¶of Coupled Nonlinear Oscillators , 2000 .
[11] Charles-Edouard Bréhier,et al. Approximation of the Invariant Measure with an Euler Scheme for Stochastic PDEs Driven by Space-Time White Noise , 2012, 1202.2707.
[12] Peter E. Kloeden,et al. The exponential integrator scheme for stochastic partial differential equations: Pathwise error bounds , 2011, J. Comput. Appl. Math..
[13] C. Conley,et al. On the ultimate behavior of orbits with respect to an unstable critical point I. Oscillating, asymptotic, and capture orbits , 1969 .
[14] P. Holmes,et al. Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle-center , 1992 .
[15] Stig Larsson,et al. Weak convergence for a spatial approximation of the nonlinear stochastic heat equation , 2012, Math. Comput..
[16] Lluís Quer-Sardanyons,et al. Weak Convergence for the Stochastic Heat Equation Driven by Gaussian White Noise , 2009, 0907.2508.
[17] Arnulf Jentzen,et al. Weak Convergence Rates for Euler-Type Approximations of Semilinear Stochastic Evolution Equations with Nonlinear Diffusion Coefficients , 2015, Found. Comput. Math..
[18] R. Kruse,et al. Duality in refined Sobolev–Malliavin spaces and weak approximation of SPDE , 2013, 1312.5893.
[19] R. Schilling,et al. Weak Order for the Discretization of the Stochastic Heat Equation Driven by Impulsive Noise , 2009, 0911.4681.
[20] P. Bernard,et al. Homoclinic orbits near saddle-center fixed points of Hamiltonian systems with two degrees of freedom , 2003 .
[21] Siqing Gan,et al. A Runge–Kutta type scheme for nonlinear stochastic partial differential equations with multiplicative trace class noise , 2011, Numerical Algorithms.
[22] P. Bernard. Homoclinic orbit to a center manifold , 2003 .
[23] J. Moser,et al. On the generalization of a theorem of A. Liapounoff , 1958 .
[24] S. Larsson,et al. Rate of weak convergence of the finite element method for the stochastic heat equation with additive noise , 2009 .
[25] Arnaud Debussche,et al. Weak approximation of stochastic partial differential equations: the nonlinear case , 2008, Math. Comput..
[26] Jacques Printems,et al. Weak order for the discretization of the stochastic heat equation , 2007, Math. Comput..
[27] P. Bernard. Homoclinic Orbits in Families of Hypersurfaces with Hyperbolic Periodic Orbits , 2002 .
[28] Eric Lombardi. Orbits Homoclinic to Exponentially Small Periodic Orbits for a Class of Reversible Systems. Application to Water Waves , 1997 .
[29] Clodoaldo Grotta Ragazzo,et al. IRREGULAR DYNAMICS AND HOMOCLINIC ORBITS TO HAMILTONIAN SADDLE CENTERS , 1997 .
[30] Xiaojie Wang,et al. Weak convergence analysis of the linear implicit Euler method for semilinear stochastic partial differential equations with additive noise , 2013 .
[31] Xiaojie Wang,et al. An Exponential Integrator Scheme for Time Discretization of Nonlinear Stochastic Wave Equation , 2013, J. Sci. Comput..
[32] P. Coullet,et al. A simple global characterization for normal forms of singular vector fields , 1987 .
[33] Xiaojie Wang,et al. Full discretisation of semi-linear stochastic wave equations driven by multiplicative noise , 2015, 1503.00073.
[34] Eric Lombardi,et al. Oscillatory Integrals and Phenomena Beyond all Algebraic Orders: with Applications to Homoclinic Orbits in Reversible Systems , 2000 .
[35] S. Sun,et al. Non–existence of truly solitary waves in water with small surface tension , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.
[36] G. Iooss,et al. Normal forms with exponentially small remainder: application to homoclinic connections for the reversible 02+iω resonance , 2004 .
[37] Helmut Rüßmann. Über das Verhalten analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung , 1964 .
[38] T. Shardlow. Weak Convergence of a Numerical Method for a Stochastic Heat Equation , 2003 .
[39] K. Kirchgässner. Wave-solutions of reversible systems and applications , 1982 .