TITLE

Construction of many Hamiltonian stationary Lagrangian surfaces in Euclidean four-space

AUTHOR(S)
Anciaux, Henri
PUB. DATE
June 2003
SOURCE
Calculus of Variations & Partial Differential Equations;Jun2003, Vol. 17 Issue 2, p105
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We make a large use of aWeierstrass representation formula to describe a variety of Hamiltonian stationary Lagrangian surfaces. Among the examples we give are the already known tori and cones, but also simply periodic cylinders, singularities of non-conical type and branch points of any order.
ACCESSION #
13604285

 

Related Articles

  • Gravitation Maneuver Using the Families of Super-Unstable Orbits around the Libration Points. Kreisman, B. B. // Cosmic Research;Jan/Feb2003, Vol. 41 Issue 1, p51 

    The families of periodic solutions to an autonomous Hamiltonian system in that part where the solutions are unstable have their specific “field of influence.” Under strong instability, the orbits that have fallen in such a “field of influence” are drawn into the family as...

  • On the passive stabilization of the equilibrium state of Lagrangian systems. He, C.; Liu, G.; Yang, L.; Tian, Y. // Acta Mechanica;1999, Vol. 134 Issue 1/2, p17 

    The idea of passive stabilization of a dynamical system whose motion is not asymptotically stable was advaved for the first time in the monograph by introducing supplementary degrees of freedom. Based on this idea, Savchenko discussed the stablization of Hamiltonian systems by a nonlinear method...

  • Singularities of Integrable and Near-Integrable Hamiltonian Systems. Bau, T.; Zung, N.T. // Journal of Nonlinear Science;Jan/Feb97, Vol. 7 Issue 1, p1 

    The aim of this Letter is to show that the singularities of integrable Hamil-tonian systems, besides being important for such systems themselves, also have many applications in the study of near-integrable systems. In particular, we will show how they are related to Kolmogorov' nondegeneracy...

  • Reversible maps in two-degrees of freedom Hamiltonian systems. Zare, K.; Tanikawa, K. // Chaos;Sep2002, Vol. 12 Issue 3, p699 

    It has been shown that a sub-class of two-degrees of freedom Hamiltonian systems possesses a reversing symmetry discovered by Birkhoff in the restricted problem of three bodies. This mixed space-time reversing symmetry, which is different from the classical time reversal symmetry, can be shared...

  • A class of integrable Hamiltonian systems whose solutions are (perhaps) all completely periodic. Calogero, F. // Journal of Mathematical Physics;Nov97, Vol. 38 Issue 11, p5711 

    Reports on a class of integrable Hamiltonian systems whose solutions are completely periodic. Evidence that the Hamiltonian system has a period that is a finite integral multiple of T+2(pie)/ohm; Hamiltonian equations of motion; Possibility in recasting the equations of motion in the modified...

  • Adler-Konstant-Symes construction, bi-Hamiltonian manifolds, and KdV equations. Guha, Partha // Journal of Mathematical Physics;Oct97, Vol. 38 Issue 10, p5167 

    Focuses on a relation between Adler-Konstant-Symes theory applied to Fordy-Kulish scheme and bi-Hamiltonian manifolds. Relation to Casati-Magri-Pedroni work on Hamiltonian formulation of the KP equation; Construction of an integrable equation associated with symmetric spaces.

  • Irreversible weak limits of classical dynamical systems. Gentili, F.; Morchio, G. // Journal of Mathematical Physics;Sep99, Vol. 40 Issue 9, p4400 

    Studies the irreversible weak limits of classical dynamical systems. Role of weak limits in simple Hamiltonian systems; Development of positive bistochastic maps characterized in terms of convergence properties of the corresponding automorphisms of the observable algebra; Definition of a...

  • The reaction volume Hamiltonian model: Further development and application. Koch, A.; Billing, G.D. // Journal of Chemical Physics;11/8/1997, Vol. 107 Issue 18, p7242 

    Studies the reaction volume Hamiltonian model. Calculation of the minimum energy path; Computation of vibrational coupling coefficients; Application of the Hamiltonian model to a four-atomic system.

  • A completely integrable Hamiltonia system. Calogero, F.; Francoise, J.-P. // Journal of Mathematical Physics;Jun96, Vol. 37 Issue 6, p2863 

    Examines a dynamical system characterized by a Hamiltonian that is completely integrable. Evolution of coordinates entailed by the Hamiltonian; Equations of motion coinciding with the Hamiltonian; Proof that the constants of motion are in involution; Reformulation of the problem via a...

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sign out of this library

Other Topics