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Publications [ 2002 ] [2001] [2000]

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

1. Geometry and Dynamics

 
 

2002


Author(s):  K.B. Blyuss
Title: Chaotic behaviour of solutions to a perturbed Korteweg-de Vries equation
Journal:  Reports on Mathematical Physics
YEAR: 2002
Abstract:  Stationary wave solutions of the perturbed Korteweg-de Vries equation are considered in the presence of external hamiltonian
perturbations. Conditions of their chaotic behaviour are studied with the help of Melnikov theory. For the homoclinic chaos Poincaré
sections are constructed to demonstrate the complicated behaviour, and Lyapunov exponents are also numerically calculated.

Author(s):  Cendra, H., J.E. Marsden, and T.S. Ratiu
Title: Cocycles and compatibility
Preprint:
YEAR: 2002

Author(s): Chossat, P.
Title: The reduction of equivariant dynamics to the orbit space for compact group actions.
Journal:  Acta Applicandae Mathematicae, 70, 71--94.
YEAR: 2002

Author(s): Chossat, P. and Armbruster, D
Title: Dynamics of polar reversals in spherical dynamics.
Journal:  To appear in  Proc. R. Soc. London.
YEAR: 2002

Author(s):  G. Cicogna and S. Walcher
Title: Convergence of normal form transformation: The role of symmetries
Journal: Acta Appl. MAth. 70,  95-111
YEAR: 2002

Author(s): R. Cushman and L. Bates
Title: The odd symplectic group in geometry
Preprint: University of Calgary
Year: June 2002
Abstract:  We describe the relation of the odd symplectic group to contact geometry and its use in the study of periodic geodesics in Riemannian geometry. 


Author(s): R. Cushman and B. Westbury
Title: Conjugacy classes in the odd symplectic group
Preprint: University of Warwick
Year: May 2002
(MASIE)Section: 1
Abstract:  In this paper we give a representative of an orbit of an element of the odd symplectic group under conjugation. We follow the ideas of Burgoyne and Cushman (J. Alg. vol. 44 (1977), 333-362) and concentrate on adjoint orbits in the Lie algebra. There are orbits which have moduli that are not eigenvalues.

Author(s):R. Cushman and M.R. Roberts
Title: Poisson structures transverse to coadjoint orbits
Journal: (to appear in Bull. Sci. Math.)
Year: 2002
Abstract:We show that the Poisson structure transverse to a coadjoint orbit in the dual of a semisimple Li
algebra has a polynomial structure matrix, as conjectured by Damianou (Bull. Sci. Math., 120, 1996, p. 195-214).


Author(s): R. Cushman and J. \'{S}niatycki
Title: Differential structure of orbit spaces
Journal: Canadian J. Math., vol. 53, 715--755
Year: 2001.
(MASIE)Section: 1
Abstract: We present a new approach to singular reduction of Hamiltonian systems with symmetries. The tools we use are the category
of differential spaces of Sikorski and the Stefan-Sussmann theorem. The former is applies to analyze the diffential structure of the spaces involved and the latter is used to prove that some of these spaces are smooth manifolds. Our main result is the identification of accessible sets of the generalized distribution spanned by the Hamiltonian vector fields of invariant functions with strata of a singular reduced space. We are also able to describe the differential structure of a singular reduced space corresponding to a coadjoint orbit which need not be locally closed. 

Author(s):  Dr\u agulete, O., L. Ornea, and T.S. Ratiu
Title: Reduction of cosphere bundles
Preprint:
YEAR: 2002

Author(s):  G. Gaeta, and S. Walcher
Title: Lie Algebras with finite dimensional polynomial centralizer
Journal: J. MAth. Anal. Appl. 269, 578-587.
YEAR: 2002

Author(s):  Ionescu D.
Title: Comparative Analysis of the Electrogravitational Kepler Problem in GRT and RTG
Journal:  Intern. J. of Non-linear Mechanics ( to appear).
YEAR: 2002

Author(s):  Ionescu D.
Title: Can BE Conserved the Concept of Homogeneozs Gravitational Field from Classical Mechanics in the Relativistic Theory of Gravitation?
Journal:  Theoretical and Mathematical Physics vol. 130 (2), 287-297.
YEAR: 2002

Author(s):  Ionescu D.
Title: The Electrogravitational Field of an Electrically Charged Mass Point and the Causality Principle in RTG
Preprint
YEAR: 2002

Author(s):  Ionescu D. and Soós E.
Title: Simultateity and non-holonomy
Preprint
YEAR: 2002

Author(s): M. Kobayashi and W.M. Oliva
Title: On the Birkhoff approach to Classical Mechanics
Preprint: CAMGSD and D.Mecanica IST- Lisbon
YEAR: 2002
(MASIE)Section : 1

Author(s):  R. Lasser, and S. Walcher
Title: Error estimates for linear compartmental systems
Journal: SIAM J. Matrix Analysis Appl. 23 (4), 1013-1024.
YEAR: 2002

Author(s):  Marsden, J.E.,  G. Misiolek, M. Perlmutter, J.-P. Ortega and T.S. Ratiu
Title: Symplectic reduction by stages
Preprint:
YEAR: 2002

Author(s):  S. Mayer, J. Scheurle and S. Walcher
Title: Normal form computations for vector fields with general linearization
Preprint
YEAR: 2002

Author(s):  Odzijewicz, A. and T.S. Ratiu
Title: Banach Lie-Poisson spaces and reduction
Preprint:
YEAR: 2002

Author(s):  W.M. Oliva
Title: Geometric Mechanics.
Book: Lect. Notes in Math, Springer-Verlag (to appear)
YEAR: 2002

Author(s):  Ortega, J.-P.
Title:  The symplectic reduced spaces of a Poisson action.
Journal: C. R. Acad. Sci. Paris Sér. I Math., 334, 999--1004.
YEAR: 2002
Notes: Available at the ArXiv.

Author(s):  Ortega, J.-P.
Title:  Singular dual pairs.
Journal: To appear in Differential Geometry and Applications
YEAR: 2002
Notes: Available at the ArXiv.

Author(s):  Ortega, J.-P.
Title:  Optimal reduction.
Preprint: Available at the ArXiv.
YEAR: 2002

Author(s):  Ortega, J.-P. and Ratiu, T. S.
Title:  A symplectic slice theorem.
Journal: Lett. Math. Phys. Physics, 59:81--93.
YEAR: 2002
Notes: Available at the ArXiv.

Author(s):  Ortega, J.-P. and T.S. Ratiu
Title: The optimal momentum map
Journal: Geometry, Dynamics, and Mechanics: 60th Birthday Volume for J.E. Marsden}, pages 329--362. P. Holmes, P. Newton, and A. Weinstein, eds., Springer-Verlag.
YEAR: 2002
Notes: Available at the ArXiv.

Author(s):  L. Sbano.
Title: Non-trivial homotopic closed orbits in Hill's region
Journal: Warwick Preprint
YEAR: 2002

Author(s):  L. Sbano.
Title: Keplerian arcs with fixed energy
Journal: Warwick Preprint
YEAR: 2002

Author(s):  L. Sbano.
Title: Odd-symplectic group in first order partial differential equations
Preprint: Warwick Preprint
YEAR: 2002

Author(s):   Sottocornola, N.
Title:  Robust homoclinic cycles in $\Bbb R^4 $
Preprint:
YEAR: 2002

 
 
 

2001


Author(s):  Cendra, H., J.E. Marsden and T.S. Ratiu
Title: Lagrangian reduction  by stages
Journal: Memoirs of the AMS, 152
YEAR: 2001

Author(s):  D R J Chillingworth, E Vicente Alonso and A A Wheeler
Title: Geometry and dynamics of a nematic liquid crystal in a uniform shear flow
Journal:  J. Physics A
YEAR: 2001

Author(s): Chossat, P.
Title: The bifurcation of heteroclinic cycles in systems of hydrodynamical type.
Journal: Dynamics of Continuous, Discrete, and  Impulsive systems}. Special issue on  Computation of normal forms
and applications.8a (4).
YEAR: 2001

Author(s): R. Cushman and J. \'{S}niatycki
Title: Differential structure of orbit spaces
Journal: Canadian J. Math., vol. 53, 715--755
Year: 2001.
Abstract: We present a new approach to singular reduction of Hamiltonian systems with symmetries. The tools we use are the category
of differential spaces of Sikorski and the Stefan-Sussmann theorem. The former is applies to analyze the diffential structure of the spaces involved and the latter is used to prove that some of these spaces are smooth manifolds. Our main result is the identification of accessible sets of the generalized distribution spanned by the Hamiltonian vector fields of invariant functions with strata of a singular reduced space. We are also able to describe the differential structure of a singular reduced space corresponding to a coadjoint orbit which need not be locally closed. 

Author(s): J. Lamb, I. Melbourne and C. Wulff
Title: General bifurcation from periodic solutions with spatio-temporal symmetries, including mode interactions and resonances.
Journal: Preprint
YEAR: 2001
URL

Author(s):  W.M. Oliva
Title: Mechanics on Riemannian Manifolds
Journal: Progr. Nonlinear Differential Equations Appl. 43, Birkhauser, 65-84.
YEAR: 2001

Author(s):  U. Scheerer, C. Wulff
Title: Reduced dynamics for momentum maps with cocycle
Journal: C. R. Acad. Sc., Série I, Math., 333, 99-104
YEAR: 2001
URL

Author(s):   Sottocornola, N.
Title:  Sur la classification des cycles homoclines.
Journal: C. R. Acad. Sci. Paris S\'er. I Math., 332, 695--698.
YEAR: 2001

Author(s):   Sottocornola, N.
Title:  Complete classification of of homoclinic cycles in $\Bbb R^4$.
Journal: C. R. Acad. Sci. Paris S\'er. I Math., 334, 859--864.
YEAR: 2001

Author(s):  S. Walcher
Title: On cooperative systems with respect to arbitrary orderings
Journal: J. Math. Analysis Appl. 263, 543-554.
YEAR: 2001

 
 
 

2000


Author(s):  Ionescu D. and Soós E.
Title: Electrogravitational Field Produced by a Charged Mass Point in RTG
Journal:  Rev. Roum. Math. P. Appl. 45, No. 2, 251-260
YEAR: 2000

Author(s):  Ionescu D. and Soós E.
Title: Consequences of the Causality Principle in the Relativistic Theory of Gravitation
Journal:  Proc. of the XXIII Intern. Workshop of High Energy Physics and Field Theory, Protvino (Russia), 180-190.
YEAR: 2000