Amadeu Delshams' recent publications (Google Scholar and ResearchGate profiles)

• Breakdown of homoclinic orbits to L₁ of the hydrogen atom in a circularly polarized microwave field
  Amadeu Delshams, Mercè Ollé, Juan Ramon Pacha, Óscar Rodríguez
  Phys. D 485 (2026), Paper No. 135031.
• Semi-analytic construction of global transfers between quasi-periodic orbits in the spatial R3BP
  Amadeu Delshams, Marian Gidea, Pablo Roldan
  Commun. Nonlinear Sci. Numer. Simul. 152 (2026), part B, Paper No. 109220, 34 pp.
• Generic global diffusion for analytic a priori unstable systems
  Amadeu Delshams, Ke Zhang
  Comm. Math. Phys. 406 (2025), no. 6, Paper No. 146, 22 pp.
• Polynomial normal forms for ODEs near a center-saddle equilibrium point
  Amadeu Delshams, Piotr Zgliczyński
  J. Differential Equations 436 (2025), Paper No. 113268, 67 pp.
• Arnold diffusion for an a priori unstable Hamiltonian system with 3+1/2 degrees of freedom
  Amadeu Delshams, Albert Granados, Rodrigo G. Schaefer
  Chaos 34(6): Paper No. 063118, 17 pp., 2024
• Exponentially Small Splitting of Separatrices Associated to 3D Whiskered Tori with Cubic Frequencies
  Amadeu Delshams, Marina Gonchenko, Pere Gutiérrez
  Comm. Math. Phys., 378(3):1931-1976, 2020 and Comm. Math. Phys., 401(1): 1059-1060, 2023
• An invitation to singular symplectic geometry
  Roisin Braddell, Amadeu Delshams, Eva Miranda, Cédric Oms, Arnau Planas
  Int. J. Geom. Methods Mod. Phys., 16:1940008, 16 pp, 2019
• Global Instability in the Restricted Planar Elliptic Three Body Problem
  Amadeu Delshams, Vadim Kaloshin, Abraham de la Rosa, Tere M. Seara
  Commun. Math. Phys., 366:1173-1228, 2019
• Quasi-periodic perturbations of heteroclinic attractor networks
  Amadeu Delshams, Antoni Guillamon, Gemma Huguet
  Chaos 28(10):103111, 19pp, 2018 (Featured article)
• Arnold diffusion for a complete family of perturbations with two independent harmonics
  Amadeu Delshams, Rodrigo G. Schaefer
  Discrete Contin. Dyn. Syst. 38(12):6047-6072, 2018
• Preface of Llavefest: A broad perspective on finite and infinite dimensional dynamical systems
  Xavier Cabré, Amadeu Delshams, Marian Gidea, Chongchun Zeng
  Discrete Contin. Dyn. Syst. 38(12):i-iii, 2018
• Mixed dynamics of 2-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies
  Amadeu Delshams, Marina Gonchenko, Sergey V. Gonchenko, J. Tomás Lázaro
  Discrete Contin. Dyn. Syst. 38(9):4483-4507, 2018
• Shadowing of non-transversal heteroclinic chains
  Amadeu Delshams, Adria Simon, Piotr Zgliczyński
  J. Differential Equations 264:3619-3663, 2018
• Examples of integrable and non integrable systems on singular symplectic manifolds
  Amadeu Delshams, Anna Kiesenhofer, Eva Miranda
  J. Geom. Phys. 115:89-97, 2017
• Corrigendum: On dynamics and bifurcations of area-preserving maps with homoclinic tangencies
  Amadeu Delshams, Marina Gonchenko, Sergey V. Gonchenko
  Nonlinearity 30(3):C2, 2017.
• Arnold diffusion for a complete family of perturbations
  Amadeu Delshams, Rodrigo G. Schaefer
  Regul. Chaotic Dyn. 22(1):78-108, 2017
• On bifurcations of homoclinic tangencies in area-preserving maps on non-orientable manifolds.
  Amadeu Delshams, Marina Gonchenko, Sergey V. Gonchenko
  Difference equations, discrete dynamical systems and applications, edited by Ll. Alsedà, J.M. Cushing, S. Elaydi, A.A. Pinto, pages 107-125, volume 180 of Springer Proc. Math. Stat., Springer, Berlin, 2016.
• Arnold's mechanism of diffusion in the spatial circular restricted three-body problem: a semi-analytical argument
  Amadeu Delshams, Marian Gidea, Pablo Roldán
  Phys. D 334:29-48, 2016
• Exponentially Small Splitting of Separatrices and Transversality Associated to Whiskered Tori with Quadratic Frequency Ratio
  Amadeu Delshams, Marina Gonchenko, Pere Gutiérrez
  SIAM J. Appl. Dyn. Syst. 15(2):981-1024, 2016.
• Instability of high dimensional Hamiltonian systems: Multiple resonances do not impede diffusion
  Amadeu Delshams, Rafael de la Llave, Tere M. Seara
  Adv. Math., 294:689-755, 2016 MR3479576
• A methodology for obtaining asymptotic estimates for the exponentially small splitting of separatrices to whiskered tori with quadratic frequencies
  Amadeu Delshams, Marina Gonchenko, Pere Gutiérrez
  Extended abstracts Spring 2014-Hamiltonian systems and celestial mechanics, virus dynamics and evolution, edited by M. Corbera, J.M. Cors, J. Llibre, A. Korobeinikov, 31-37, Trends Math. Res. Perspect. CRM Barc., 4, Birkhäuser/Springer, Cham, 2015.
• On dynamics and bifurcations of area-preserving maps with homoclinic tangencies
  Amadeu Delshams, Marina Gonchenko, Sergey V. Gonchenko
  Nonlinearity 28(9):3027-3071, 2015. MR3403390
• On Bifurcations of Area-preserving and Nonorientable Maps with Quadratic Homoclinic Tangencies
  Amadeu Delshams, Marina Gonchenko, Sergey V. Gonchenko
  Regul. Chaotic Dyn. 19(6):702-717, 2014.
• Continuation of the Exponentially Small Transversality for the Splitting of Separatrices to a Whiskered Torus with Silver Ratio
  Amadeu Delshams, Marina Gonchenko, Pere Gutiérrez
  Regul. Chaotic Dyn. 19(6):663-680, 2014.
• Exponentially Small Lower Bounds for the Splitting of Separatrices to Whiskered Tori with Frequencies of Constant Type
  Amadeu Delshams, Marina Gonchenko, Pere Gutiérrez
  Internat. J. Bifur. Chaos Appl. Sci. Engrg. 24, No. 8 (2014) 1440011 (12 pages)
• Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tori with quadratic and cubic frequencies
  Amadeu Delshams, Marina Gonchenko, Pere Gutiérrez
  Electron. Res. Announc. Math. Sci. 21:41-61, 2014
• Abundance of attracting, repelling and elliptic periodic orbits in two-dimensional reversible maps
  A. Delshams, S.V. Gonchenko, V.S. Gonchenko, J.T. Lázaro, O. Sten'kin
  Nonlinearity 26:1-33, 2013
• Transversality of homoclinic orbits to hyperbolic equilibria in a Hamiltonian system, via the Hamilton-Jacobi equation
  Amadeu Delshams, Pere Gutiérrez, Juan R. Pacha
  Physica D 243:64-85, 2013
• Transition map and shadowing lemma for normally hyperbolic invariant manifolds
  Amadeu Delshams, Marian Gidea, Pablo Roldán
  Discrete Contin. Dyn. Syst. 33(3):1089-1112, 2013
• A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems
  Amadeu Delshams, Gemma Huguet
  J. Differential Equations, 250:2601-2623, 2011 MR2756078 MSN citations Google Academic
• Transverse intersections between invariant manifolds of doubly hyperbolic invariant tori, via the Poincaré-Mel'nikov method.
  A. Delshams, P. Gutiérrez, O. Koltsova, J. R. Pacha
  Regul. Chaotic Dyn., 15(2-3):222-236, 2010 MR 2011d:37100 MSN citations
• Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems
  Amadeu Delshams, Gemma Huguet
  Nonlinearity, 22:1997-2077, 2009 MR 2010h:37136 MSN citations Google Academic
• Euler's beta integral in Pietro Mengoli's works
  Ma Rosa Massa, Amadeu Delshams
  Arch. Hist. Exact Sci., 3:325-356, 2009 MR 2501200 MSN citations Google Academic

• Geometric approaches to the problem of instability in Hamiltonian systems. An informal presentation
  Amadeu Delshams, Marian Gidea, Rafael de la Llave, Tere M. Seara
  Hamiltonian dynamical systems and applications, edited by Walter Craig, 285-336, NATO Sci. Peace Secur. Ser. B Phys. Biophys., Springer, Dordrecht, 2008 MR 2009k:37132 MSN citations Google Academic
• Computing the scattering map in the spatial Hill's problem
  Amadeu Delshams, Josep Masdemont, Pablo Roldán
  Discrete Contin. Dyn. Syst. Ser. B, 10(2-3):455-483, 2008 MR 2425052 MSN citations Google Academic
• Geometric properties of the scattering map of a normally hyperbolic invariant manifold
  Amadeu Delshams, Rafael de la Llave, Tere M. Seara
  Adv. Math., 217(3):1096-1153, 2008 MR 2008m:37100 MSN citations Google Academic
• The scattering map in the planar Restricted Three Body Problem
  E. Canalias, A. Delshams, J.J. Masdemont and P. Roldán
  Celestial Mech. Dynam. Astronom., 95(1-4):155-171, 2006 MR 2007h:70021 MSN citations Google Academic
• Orbits of unbounded energy in quasi-periodic perturbations of geodesic flows
  Amadeu Delshams, Rafael de la Llave, Tere M. Seara
  Adv. Math., 202(1):64-188, 2006 MR 2007a:37070 MSN citations Google Academic
• Homoclinic Orbits for Invariant Tori of Nearly Integrable Hamiltonian Systems
  O. Yu. Koltsova, L. M. Lerman, A. Delshams, P. Gutiérrez
  Dokl. Math., 73(2):217-220, 2006 MR 2008k:371236 MSN citations Google Academic
• A Geometric Mechanism for Diffusion in Hamiltonian Systems Overcoming the large Gap Problem: Heuristics and Rigorous Verification on a Model
  Amadeu Delshams, Rafael de la Llave, Tere M. Seara
  Mem. Amer. Math. Soc., 179(844):1-141, 2006 MR 2184276 MSN citations Google Academic
• Poincaré, creador de los métodos todavía modernos en las ecuaciones diferenciales y en la mecánica celeste
  Amadeu Delshams
  Arbor: Ciencia, Pensamiento y Cultura, CLXXVII(704):669-689, 2004
• Exponentially small splitting of separatrices for whiskered tori in Hamiltonian systems
  Amadeu Delshams, Pere Gutiérrez
  J. Math. Sci., 128(2):2726-2746, 2005 Google Academic
• Homoclinic orbits to invariant tori near a homoclinic orbit to center-center-saddle equilibrium
  Oksana Koltsova, Lev Lerman, Amadeu Delshams, Pere Gutiérrez
  Phys. D., 201(3-4):268-290, 2005 MR 2005m:37140 MSN citations Google Academic
• Pseudo-normal form near saddle-center or saddle-focus equilibria
  Amadeu Delshams and J. Tomás Lázaro
  J. Differential Equations, 208(2):312-343, 2005 MR 2005h:34101 MSN citations Google Academic
• Exponentially small splitting for whiskered tori in hamiltonian systems: flow-box coordinates and upper bounds
  Amadeu Delshams, Pere Gutiérrez, Tere M. Seara
  Discrete Contin. Dyn. Syst., 11(4):785-826, 2004 MR 2005j:37102 MSN citations Google Academic
• Exponentially small splitting for whiskered tori in hamiltonian systems: continuation of transverse homoclinic orbits
  Amadeu Delshams, Pere Gutiérrez
  Discrete Contin. Dyn. Syst., 11(4):757-783, 2004 MR 2005j:37101 MSN citations Google Academic
• Persistence of homoclinic orbits for billiards and twist maps
  Sergey Bolotin, Amadeu Delshams, Rafael Ramírez-Ros
  Nonlinearity, 17(4):1153-1177, 2004 MR 2005d:37126 MSN citations Google Academic
• Mathematical modelling and simulation of cotransport phenomena through flat sheet-supported liquid membranes
  G. Benzal, A. Kumar, A. Delshams, A. M. Sastre
  Hydrometallurgy, 74(1-2):117-30, 2004 MR 2024440 MSN citations Google Academic
• A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: announcement of results
  Amadeu Delshams, Rafael de la Llave, Tere M. Seara
  Electron. Res. Announc. Amer. Math. Soc., 9:125-134, 2003
• Simulation of non-linear flow density in transition state from the mathematical model of the diffusion of metal anions through a flat sheet supported liquid membrane
  G. Benzal, A. Kumar, A. M. Sastre, A. Delshams
  J. Math. Chem., 34(1-2):1-27, 2003
• Exponentially small splitting of separatrices for whiskered tori in Hamiltonian systems
  Amadeu Delshams, Pere Gutiérrez
  Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 300:87-121, 2003
• A pseudo-normal form for planar vector fields
  Amadeu Delshams, Antoni Guillamon, J. Tomás Lázaro
  Qual. Theory Dyn. Syst., 3(1):51-82. 2002
• Homoclinic billiard orbits inside symmetrically perturbed ellipsoids
  Amadeu Delshams, Yuri Fedorov, Rafael Ramírez-Ros
  Nonlinearity, 14:1141-1195, 2001
• Splitting potential and Poincaré-Melnikov method for whiskered tori in Hamiltonian Systems
  Amadeu Delshams, Pere Gutiérrez
  J. Nonlinear Sci., 10(4):433-476, 2000.
• KAM theory and a partial justification of Greene's criterion for non-twist maps
  Amadeu Delshams, Rafael de la Llave
  SIAM J. Math. Anal., 31(6):1235-1269, 2000.
• A geometric approach to the existence of orbits with unbounded energy in generic periodic perturbations by a potential of generic geodesic flows of T²
  Amadeu Delshams, Rafael de la Llave, Tere M. Seara
  Comm. Math. Phys., 209(2):353-392, 2000.
• Unbounded growth of energy in periodic perturbations of geodesic flows of the torus
  Amadeu Delshams, Rafael de la Llave, Tere M. Seara
  J. Delgado, E.A. Lacomba, E. Pérez-Chavela, J. Llibre, editors, Hamiltonian systems and Celestial mechanics (HAMSYS-98), volume 6 of World Scientific Monograph Series in Mathematics, World Sci. Publishing, 2000.
  Abstract (ASCII file), PostScript (330 Kb), zipped version (102 Kb).
• Splitting and Melnikov potentials in Hamiltonian systems
  Amadeu Delshams, Pere Gutiérrez
  J. Delgado, E.A. Lacomba, E. Pérez-Chavela, J. Llibre, editors, Hamiltonian systems and Celestial mechanics (HAMSYS-98), volume 6 of World Scientific Monograph Series in Mathematics, World Sci. Publishing, 2000.
  Abstract (ASCII file), PostScript (277 Kb), zipped version (106 Kb).
• Homoclinic orbits to invariant tori in Hamiltonian systems
  Amadeu Delshams, Pere Gutiérrez
  C.K.R.T. Jones, A. Khibnik, editors, Multiple-Time-Scale Dynamical Systems, pp. 1-28, volume 122 of IMA Vol. Math. Appl., Springer-Verlag, Berlin, 2000.
  Abstract (ASCII file), Pdf version.
• Singular separatrix splitting and the Poincaré-Melnikov method for area preserving maps
  Amadeu Delshams, Rafael Ramírez-Ros
  B. Fiedler, K. Gröger, J. Sprekels, editors, EQUADIFF 99, pp. 941-946, World Sci. Publishing, 2000.
  Abstract (ASCII file), Pdf version.
• Singular separatrix splitting and Melnikov method: An experimental study
  Amadeu Delshams, Rafael Ramírez-Ros
  Experiment. Math., 8(1):29-48, 1999.
• Splitting of separatrices in Hamiltonian systems and symplectic maps
  Amadeu Delshams, Tere M. Seara, Rafael Ramírez-Ros
  C. Simó, editor, Hamiltonian Systems with Three or More Degrees of Freedom, volume 533 of NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., pp. 39-54. Kluwer, Dordrecht, 1999. MR 2000j:37075
  Abstract (ASCII file), PostScript (262 Kb), zipped version (102 Kb).
• Splitting of separatrices for (fast) quasiperiodic forcing
  Amadeu Delshams, Vassili Gelfreich, Àngel Jorba, Tere M. Seara
  C. Simó, editor, Hamiltonian Systems with Three or More Degrees of Freedom, volume 533 of NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., pp. 367-371. Kluwer, Dordrecht, 1999. CMP 1720914
  Abstract (ASCII file), PostScript (108 Kb), zipped version (42 Kb).
• Exponentially small estimates for KAM theorem near an elliptic equilibrium point
  Amadeu Delshams, Pere Gutiérrez
  C. Simó, editor, Hamiltonian Systems with Three or More Degrees of Freedom, volume 533 of NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., pp. 386-390. Kluwer, Dordrecht, 1999. MR 2000g:37087
  Abstract (ASCII file), PostScript (84 Kb), zipped version (35 Kb).
• Effective stability in reversible systems
  Amadeu Delshams, José Tomás Lázaro
  C. Simó, editor, Hamiltonian Systems with Three or More Degrees of Freedom, volume 533 of NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., pp. 453-457. Kluwer, Dordrecht, 1999. MR 2000g:37088
  Abstract (ASCII file), PostScript (96 Kb), zipped version (39 Kb).
• Psi-series, singularities of solutions and integrability of polynomial systems
  Arnau Mir, Amadeu Delshams
  C. Simó, editor, Hamiltonian Systems with Three or More Degrees of Freedom, volume 533 of NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., pp. 504-508. Kluwer, Dordrecht, 1999. CMP 1720937
  Abstract (ASCII file), PostScript (71 Kb), zipped version (30 Kb).
• Poincaré-Melnikov-Arnold method for twist maps
  Amadeu Delshams, Rafael Ramírez-Ros
  C. Simó, editor, Hamiltonian Systems with Three or More Degrees of Freedom, volume 533 of NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., pp. 533-537. Kluwer, Dordrecht, 1999. MR 2000g:37101
  Abstract (ASCII file), PostScript (125 Kb), zipped version (54 Kb).
• Exponentially small splitting of separatrices for perturbed integrable standard-like maps
  Amadeu Delshams, Rafael Ramírez-Ros
  J. Nonlinear Sci., 8(3):317-352, 1998.
• Homoclinic orbits of twist maps and billiards
  Amadeu Delshams, Rafael Ramírez-Ros
  D. Bambusi and G. Gaeta, editors, Symmetry and Perturbation Theory, Quaderno GNFM, 54, pp. 46-86. Firenze, Italy, 1998.
• Singular splitting of separatrices for the perturbed McMillan map
  Amadeu Delshams, Rafael Ramírez-Ros
  XV Congress on Differential Equations and Applications/V Congress on Applied Mathematics, Vol. I, II (Vigo, 1997), pp. 243-248. Univ. Vigo, Vigo, 1998. MR 99e:58156
  Abstract (ASCII file), PostScript (127 Kb), zipped version (52 Kb).
• Homoclinic orbits of twist maps and billiards
  Amadeu Delshams, Rafael Ramírez-Ros
  D. Bambusi and G. Gaeta, editors, Symmetry and Perturbation Theory, Quaderno GNFM, 54, pp. 46-86. Firenze, Italy, 1998.
  Abstract (ASCII file), PostScript (644 Kb), zipped version (230 Kb).
• Melnikov potential for exact symplectic maps
  Amadeu Delshams, Rafael Ramírez-Ros
  Comm. Math. Phys., 190(1):213-245, 1997.
• Splitting of separatrices in Hamiltonian systems with one and a half degrees of freedom
  Amadeu Delshams, Tere M. Seara
  Math. Phys. Electron. J., 3(1): 1-40, 1997.
• Exponentially small splitting of separatrices under fast quasiperiodic forcing
  Amadeu Delshams, Vassili Gelfreich, Àngel Jorba, Tere M. Seara
  Comm. Math. Phys., 189(1): 35-71, 1997.
• Psi-series of quadratic vector fields on the plane
  Amadeu Delshams, Arnau Mir
  Publ. Mat., 41(1):101-125, 1997.
• Lower and upper bounds for the splitting of separatrices of the pendulum under a fast quasiperiodic forcing
  Amadeu Delshams, Vassili Gelfreich, Àngel Jorba, Tere M. Seara
  Electron. Res. Announc. Amer. Math. Soc., 3:1-10, 1997.
• Estimates on invariant tori near an elliptic equilibrium point of a Hamiltonian system
  Amadeu Delshams, Pere Gutiérrez
  J. Differential Equations, 131:277-303, 1996.
• Effective stability and KAM theory
  Amadeu Delshams, Pere Gutiérrez
  J. Differential Equations, 128:415-490, 1996.
• Poincaré-Melnikov-Arnold method for analytic planar maps
  Amadeu Delshams, Rafael Ramírez-Ros
  Nonlinearity, 9:1-26, 1996.
• On Birkhoff's conjecture about convex billiards
  Amadeu Delshams, Rafael Ramírez-Ros
  M. Sofonea and J.-N. Corvellec, editors, Proceedings of the 2nd Catalan Days on Applied Mathematics (Odeillo, 1995), Collect. Études, pp. 85-94. Presses Univ. de Perpignan, Perpignan, 1995.
• An asymptotic expression for the splitting of separatrices of the rapidly forced pendulum
  Amadeu Delshams, Tere M. Seara
  Comm. Math. Phys., 150(3): 433-463, 1992.
• Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three-body problem
  Antonio Giorgilli, Amadeu Delshams, Ernest Fontich, Luigi Galgani, Carles Simó
  J. Differential Equations, 77(1):167-198, 1989.