[*] Amadeu Delshams, Marina Gonchenko, and Pere Gutiérrez. Exponentially small splitting of separatrices and transversality associated to whiskered tori with quadratic frequency ratio. SIAM J. Appl. Dyn. Syst., 15(2):981--1024, 2016. [ DOI ]
[*] A. Delshams, M. Gonchenko, and P. Gutiérrez. A methodology for obtaining asymptotic estimates for the exponentially small splitting of separatrices to whiskered tori with quadratic frequencies. In M. Corbera, J.M. Cors, J. Llibre, and A. Korobeinikov, editors, Extended Abstracts Spring 2014: Hamiltonian Systems and Celestial Mechanics; Virus Dynamics and Evolution, volume 4 of Research Perspectives CRM Barcelona (Trends. Math.), pages 31--37. Birkhäuser, Basel, 2015. [ DOI ]
[*] Amadeu Delshams, Marina Gonchenko, and Pere Gutiérrez. Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio. Regul. Chaotic Dyn., 19(6):663--680, 2014. [ DOI ]
[*] Amadeu Delshams, Marina Gonchenko, and Pere Gutiérrez. Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tori with quadratic and cubic frequencies. Electron. Res. Announc. Math. Sci., 21:41--61, 2014. [ DOI ]
[*] Amadeu Delshams, Marina Gonchenko, and Pere Gutiérrez. Exponentially small lower bounds for the splitting of separatrices to whiskered tori with frequencies of constant type. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 24(8):1440011, 12, 2014. [ DOI ]
[*] Amadeu Delshams, Pere Gutiérrez, and Juan R. Pacha. Transversality of homoclinic orbits to hyperbolic equilibria in a Hamiltonian system, via the Hamilton-Jacobi equation. Phys. D, 243:64--85, 2013. [ DOI ]
[*] A. Delshams, P. Gutiérrez, O. Koltsova, and J. R. Pacha. Transverse intersections between invariant manifolds of doubly hyperbolic invariant tori, via the Poincaré-Mel'nikov method. Regul. Chaotic Dyn., 15(2-3):222--236, 2010. [ DOI ]
[*] O. Yu. Koltsova, L. M. Lerman, A. Delshams, and P. Gutierres. Homoclinic orbits to invariant tori of a nearly integrable Hamiltonian system. Dokl. Akad. Nauk, 407(3):307--310, 2006.
[*] Oksana Koltsova, Lev Lerman, Amadeu Delshams, and Pere Gutiérrez. Homoclinic orbits to invariant tori near a homoclinic orbit to center-center-saddle equilibrium. Phys. D, 201(3-4):268--290, 2005. [ DOI ]
[*] A. Delshams and P. Gutiérrez. Exponentially small splitting of separatrices for whiskered tori in Hamiltonian systems. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 300(Teor. Predst. Din. Sist. Spets. Vyp. 8):87--121, 287, 2003. [ DOI ]
[*] Amadeu Delshams, Pere Gutiérrez, and Tere M. Seara. Exponentially small splitting for whiskered tori in Hamiltonian sysems: flow-box coordinates and upper bounds. Discrete Contin. Dyn. Syst., 11(4):785--826, 2004. [ DOI ]
[*] Amadeu Delshams and Pere Gutiérrez. Exponentially small splitting for whiskered tori in Hamiltonian systems: continuation of transverse homoclinic orbits. Discrete Contin. Dyn. Syst., 11(4):757--783, 2004. [ DOI ]
[*] Amadeu Delshams and Pere Gutiérrez. Homoclinic orbits to invariant tori in Hamiltonian systems. In Multiple-time-scale dynamical systems (Minneapolis, MN, 1997), volume 122 of IMA Vol. Math. Appl., pages 1--27. Springer, New York, 2001. [ DOI ]
[*] Amadeu Delshams and Pere Gutiérrez. Splitting and Melnikov potentials in Hamiltonian systems. In Hamiltonian systems and celestial mechanics (Pátzcuaro, 1998), volume 6 of World Sci. Monogr. Ser. Math., pages 111--137. World Sci. Publ., River Edge, NJ, 2000. [ DOI ]
[*] A. Delshams and P. Gutiérrez. Splitting potential and the Poincaré-Melnikov method for whiskered tori in Hamiltonian systems. J. Nonlinear Sci., 10(4):433--476, 2000. [ DOI ]
[*] Amadeu Delshams and Pere Gutiérrez. Exponentially small estimates for KAM theorem near an elliptic equilibrium point. In Hamiltonian systems with three or more degrees of freedom (S'Agaró, 1995), volume 533 of NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., pages 386--390. Kluwer Acad. Publ., Dordrecht, 1999.
[*] Amadeu Delshams and Pere Gutiérrez. Estimates on invariant tori near an elliptic equilibrium point of a Hamiltonian system. J. Differential Equations, 131(2):277--303, 1996. [ DOI ]
[*] Amadeu Delshams and Pere Gutiérrez. Effective stability and KAM theory. J. Differential Equations, 128(2):415--490, 1996. [ DOI ]
[*] P. Gutiérrez. Estabilitat efectiva i tors invariants de sistemes hamiltonians quasi-integrables. PhD thesis, Univ. Barcelona, 1996. [ URL ]
[*] Amadeu Delshams and Pere Gutiérrez. Nekhoroshev and KAM theorems revisited via a unified approach. In Hamiltonian mechanics (Toruń, 1993), volume 331 of NATO Adv. Sci. Inst. Ser. B Phys., pages 299--306. Plenum, New York, 1994.
[*] Amadeo Delshams and Pere Gutiérrez. Effective stability for nearly integrable Hamiltonian systems. In International Conference on Differential Equations, Vol. 1, 2 (Barcelona, 1991), pages 415--420. World Sci. Publ., River Edge, NJ, 1993.