Found 83 Documents (Results 1–83)
Distribution of stable islands within chaotic areas in the non-hyperbolic and hyperbolic regimes in the Hénon-Heiles system. (English) Zbl 1517.70040
Periodic solutions in the Hénon-Heiles rotating system. (English) Zbl 1514.70021
Ahusborde, É. (ed.) et al., Fifteenth international conference Zaragoza-Pau on mathematics and its applications. Proceedings of the conference, Jaca, Spain, September 10–12, 2018. Zaragoza: Prensas de la Universidad de Zaragoza. Monogr. Mat. García Galdeano 42, 165-172 (2019).
Detection of periodic orbits in Hamiltonian systems using Lagrangian descriptors. (English) Zbl 1386.37061
Systematic computer-assisted proof of branches of stable elliptic periodic orbits and surrounding invariant tori. (English) Zbl 1376.65149
Exact solutions in the invariant manifolds of the generalized integrable Hénon-Heiles system and exact traveling wave solutions of Klein-Gordon-Schrödinger equations. (English) Zbl 1358.34004
Lyapunov stability for a generalized Hénon-Heiles system in a rotating reference frame. (English) Zbl 1338.37068
MSC:
37J25
The cohesiveness of G-symplectic methods. (English) Zbl 1330.65192
Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca)
Generic hyperelliptic Prym varieties in a generalized Hénon-Heiles system. (English) Zbl 1346.14096
Reviewer: Shigeki Matsutani (Nagasaki)
Consecutive Rosochatius deformations of the Garnier system and the Hénon-Heiles system. (English) Zbl 1449.37039
Bifurcations from one-parameter families of symmetric periodic orbits in reversible systems. (English) Zbl 1277.37081
Nonlinearity 26, No. 5, 1345-1360 (2013); erratum ibid No. 6, 1823 (2013).
Reviewer: Iliya Iliev (Sofia)
Comparing the efficiency of numerical techniques for the integration of variational equations. (English) Zbl 1306.65286
Periodic orbits and non-integrability of Hénon-Heiles systems. (English) Zbl 1296.34106
Reviewer: Xiang Zhang (Shanghai)
Stabilization of solutions of dissipative Hamiltonian systems. (English) Zbl 1242.34119
Reviewer: Martin Rasmussen (London)
Higher-order Melnikov method and chaos for two-degree-of-freedom Hamiltonian systems with saddle-centers. (English) Zbl 1213.37092
Reviewer: Dorin Andrica (Riyadh)
Simple conservative, autonomous, second-order chaotic complex variable systems. (English) Zbl 1193.34087
On Hamiltonian potentials with quartic polynomial normal variational equations. (English) Zbl 1180.37079
Construction of special solutions for nonintegrable systems. (English) Zbl 1120.34003
Reviewer: Nikolay Vasilye Grigorenko (Kyïv)
Computable chaos in dynamical systems. (Berechenbares Chaos in dynamischen Systemen.) (German) Zbl 1096.65128
Basel: Birkhäuser (ISBN 3-7643-7550-7/pbk). xii, 264 p. (2006).
Reviewer: Boris V. Loginov (Ul’yanovsk)
No polar coordinates. (Based on lectures by Richard Cushman). (English) Zbl 1192.37076
Montaldi, James (ed.) et al., Geometric mechanics and symmetry; the Peyresq lectures. Lecture notes from the European Summer Schools in Geometric Mechanics held in Peyresq, 2000/2001. Cambridge: Cambridge University Press (ISBN 0-521-53957-9/pbk). London Mathematical Society Lecture Note Series 306, 211-301 (2005).
Reviewer: Jesús Marín-Solano (Barcelona)
Algebraic methods for determining Hamiltonian Hopf bifurcations in three-degree-of-freedom systems. (English) Zbl 1078.37041
Single-valued and multivalued solutions for the generalized Hénon-Heiles system with an additional nonpolynomial term. (English) Zbl 1112.37044
Mladenov, Ivaïlo M.(ed.) et al., Proceedings of the 6th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 3–10, 2004. Sofia: Bulgarian Academy of Sciences (ISBN 954-84952-9-5/pbk). 297-309 (2005).
Reviewer: Nicolai K. Smolentsev (Kemerovo)
A conservative numerical integration algorithm for integrable Henon-Heiles system. (English) Zbl 1095.37044
Nikitin, A.G.(ed.) et al., Proceedings of the fifth international conference on symmetry in nonlinear mathematical physics, Kyïv, Ukraine, June 23–29, 2003. Part 1. Kyïv: Institute of Mathematics of NAS of Ukraine (ISBN 966-02-3225-X). Proceedings of the Institute of Mathematics of the National Academy of Sciences of Ukraine. Mathematics and its Applications. 50(1), 444-449 (2004).
Reviewer: M. O. Nesterenko (Kyïv)
Constructing solutions for the generalized Hénon-Heiles system through the Painlevé test. (English) Zbl 1178.37054
Theor. Math. Phys. 135, No. 3, 792-801 (2003); translation from Teor. Mat. Fiz. 135, No. 3, 409-419 (2003).
The Henon-Heiles differential system and Prym varieties. (Le système différentiel de Hénon-Heiles et les variétés de Prym.) (French) Zbl 1070.37040
Reviewer: Igor Potemine (Toulouse)
Integrability and nonintegrability of Hamiltonian systems. (Intégrabilité et non-intégrabilité de systèmes hamiltoniens.) (French) Zbl 1050.37028
Bourbaki seminar. Volume 2000/2001. Exposés 880-893. Paris: Société Mathématique de France (ISBN 2-85629-130-9/pbk). Astérisque 282, 113-135, Exp. No. 884 (2002).
Reviewer: Claudio Bartocci (Genova)
A modern approach to classical mechanics. (English) Zbl 1046.70001
Singapore: World Scientific (ISBN 981-238-213-5/hbk). xii, 442 p. (2002).
Reviewer: Mira-Cristiana Anisiu (Cluj-Napoca)
Meromorphic nonintegrability of Hamiltonian systems. (English) Zbl 1019.37034
Reviewer: Simos Ichtiaroglou (Thessaloniki)
Normal form methods for symbolic creation of approximate solutions of nonlinear dynamical systems. (English) Zbl 0986.65123
Symbolic dynamics for the Hénon-Heiles Hamiltonian on the critical level. (English) Zbl 1018.37006
Reviewer: Simos Ichtiaroglou (Thessaloniki)
Performance of two methods for solving separable Hamiltonian systems. (English) Zbl 0971.65114
Reviewer: Werner M.Seiler (Mannheim)
Properties of the canonical transformations of the time for the Toda lattice and the Hénon-Heiles system. (English) Zbl 0969.37026
Reviewer: Mircea Puta (Timişoara)
Caustics, cusps and chaos in Hamiltonian systems. (English) Zbl 0987.70014
Simó, Carles (ed.), Hamiltonian systems with three or more degrees of freedom. Proceedings of the NATO Advanced Study Institute, S’Agaró, Spain, June 19-30, 1995. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 533, 588-591 (1999).
Reviewer: Simos Ichtiaroglou (Thessaloniki)
Mel’nikov vector and singularity analysis of periodically perturbed 2 D. O. F. Hamiltonian systems. (English) Zbl 0964.37039
Simó, Carles (ed.), Hamiltonian systems with three or more degrees of freedom. Proceedings of the NATO Advanced Study Institute, S’Agaró, Spain, June 19-30, 1995. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 533, 544-548 (1999).
Reviewer: Jörg Härterich (Berlin)
The Lax pairs for the Holt system. (English) Zbl 0955.37038
Reviewer: Samir Musaev (Baku)
Bäcklund transformations for many-body systems related to KdV. (English) Zbl 0952.37054
Reviewer: Samir Musayev (Baku)
Computation of normal forms of Hamiltonian systems in the presence of Poisson commuting integrals. (English) Zbl 0939.65138
Reviewer: Werner M.Seiler (Mannheim)
Integrability of the Hénon-Heiles system. (English) Zbl 0952.37034
Reviewer: Samir Musayev (Baku)
MSC:
37K10
35Q58
Adiabatic invariants of generalized Hénon-Heiles Hamiltonian system and the structure of chaotic motion. (English) Zbl 0921.58027
Reviewer: Valerie Samoilenko (Kyïv)
On the non-integrability of quartic potentials. (Sur la non-intégrabilité de potentiels quartiques.) (French) Zbl 0907.58019
Reviewer: Raul Ibañez (Bilbão)
Transversal splitting of the separatrix manifolds of generalized Henon-Heiles Hamiltonian system. (English) Zbl 0924.34031
Reviewer: Valerie Samoilenko (Kyïv)
Transversal splitting of the separatrix manifolds of generalized Henon-Heiles Hamiltonian system. (English) Zbl 0901.34052
Reviewer: Valerie Samoilenko (Kyïv)
Quasi-point separation of variables for the Hénon-Heiles system and a system with a quartic potential. (English) Zbl 0905.58011
On the integrability of stationary and restricted flows of the KdV hierarchy. (English) Zbl 0870.35092
Lax pairs in the Henon-Heiles and related families. (English) Zbl 0838.58015
Dumas, H. S. (ed.) et al., Hamiltonian dynamical systems: history, theory, and applications. Proceedings of the international conference held at the University of Cincinnati, OH (USA), March 1992. New York, NY: Springer-Verlag. IMA Vol. Math. Appl. 63, 89-98 (1995).
Reviewer: S.Nenov (Sofia)
Squared eigenfunction coordinates and stationary flows. (English) Zbl 0982.35093
Makhanov, V. G. (ed.) et al., Nonlinear evolution equations and dynamical systems. NEEDS ’94. Proceedings of the 10th international workshop, Los Alamos, NM, USA, September 11-18, 1994. Singapore: World Scientific. 9-15 (1995).
MSC:
35Q53
37K05
A connection between the Henon-Heiles system and the Garnier system. (English) Zbl 0850.35104
Theor. Math. Phys. 99, No. 3, 796-802 (1994) and Teor. Mat. Fiz. 99, No. 3, 552-559 (1994).
Jacobi polynomials and Lax representation for completely integrable dynamical systems. (English. Russian original) Zbl 0866.35106
Ukr. Math. J. 46, No. 8, 1198-1201 (1994); translation from Ukr. Mat. Zh. 46, No. 8, 1088-1091 (1994).
Classical Poisson structure for a hierarchy of one-dimensional particle systems separable in parabolic coordinates. (English) Zbl 0952.37026
Reviewer: Samir Musayev (Baku)
On the Padé approximations to the Birkhoff-Gustavson normal form. (English) Zbl 0847.58039
Reviewer: N.Medvedeva (Chelyabinsk)
Applications of the generalized symmetry method. (English) Zbl 0790.34012
Ibragimov, N. Kh. (ed.) et al., Modern group analysis: Advanced analytical and computational methods in mathematical physics. Proceedings of the international workshop Acireale, Catania, Italy, October 27-31, 1992. Dordrecht: Kluwer Academic Publishers. 43-53 (1993).
Separability and Lax pairs for Hénon-Heiles system. (English) Zbl 0784.58029
Reviewer: B.Fuchssteiner (Paderborn)
Direct integration of generalized Lie symmetries of nonlinear Hamiltonian systems with two degrees of freedom: Integrability and separability. (English) Zbl 0760.35050
Symplectic phase flow approximation for the numerical integration of canonical systems. (English) Zbl 0734.65058
Numer. Math. (to appear).
Reviewer: S.Miesbach and H.J.Pesch
Symplectic phase flow approximation for the numerical integration of canonical systems. (English) Zbl 0755.65074
Improved accuracy of the Birkhoff-Gustavson normal form and its convergence properties. (English) Zbl 0766.58049
On a bifurcation in the quantum system for an approximation to the Hénon-Heiles system. (English) Zbl 0681.58031
Note on the generalized Hénon-Heiles system. (English) Zbl 0672.58013
Reviewer: B.Valiño Alonso
The Kowalewski and Hénon-Heiles motions as Manakov geodesic flows on SO(4) - a two-dimensional family of Lax pairs. (English) Zbl 0647.58022
Reviewer: E.D.Belokolos
Invariance and integrability: Hénon-Heiles and two coupled quartic anharmonic oscillator systems. (English) Zbl 0627.58025
Reviewer: P.Kramer
Non-integrability of Hénon-Heiles system and a theorem of Ziglin. (English) Zbl 0577.58016
Reviewer: G.Warnecke
Explicit integrability for Hamiltonian systems and the Painlevé conjecture. (English) Zbl 0566.70020
Reviewer: M.Kummer
Branching of solutions and the nonexistence of first integrals in Hamiltonian mechanics. II. (English. Russian original) Zbl 0518.58016
Funct. Anal. Appl. 17, 6-17 (1983); translation from Funkts. Anal. Prilozh. 17, No. 1, 8-23 (1983).
Analytic structure of the Henon-Heiles Hamiltonian in integrable and nonintegrable regimes. (English) Zbl 0492.70019
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