54 research outputs found
On the algebraic invariant curves of plane polynomial differential systems
We consider a plane polynomial vector field of degree
. To each algebraic invariant curve of such a field we associate a compact
Riemann surface with the meromorphic differential . The
asymptotic estimate of the degree of an arbitrary algebraic invariant curve is
found. In the smooth case this estimate was already found by D. Cerveau and A.
Lins Neto [Ann. Inst. Fourier Grenoble 41, 883-903] in a different way.Comment: 10 pages, Latex, to appear in J.Phys.A:Math.Ge
How to find discrete contact symmetries
This paper describes a new algorithm for determining all discrete contact
symmetries of any differential equation whose Lie contact symmetries are known.
The method is constructive and is easy to use. It is based upon the observation
that the adjoint action of any contact symmetry is an automorphism of the Lie
algebra of generators of Lie contact symmetries. Consequently, all contact
symmetries satisfy various compatibility conditions. These conditions enable
the discrete symmetries to be found systematically, with little effort
Critical behavior of magnetic systems with extended impurities in general dimensions
We investigate the critical properties of d-dimensional magnetic systems with
quenched extended defects, correlated in
dimensions (which can be considered as the dimensionality of the
defects) and randomly distributed in the remaining dimensions;
both in the case of fixed dimension d=3 and when the space dimension
continuously changes from the lower critical dimension to the upper one. The
renormalization group calculations are performed in the minimal subtraction
scheme. We analyze the two-loop renormalization group functions for different
fixed values of the parameters . To this end, we apply the
Chisholm-Borel resummation technique and report the numerical values of the
critical exponents for the universality class of this system.Comment: 8 figures. To appear in Phys. Rev.
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