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On Lie point symmetries in mechanics
"... this paper we want to present some considerations on the symmetry properties of the dynamical problems which are expressed as systems either of secondorder ordinary differential equations in NewtonLagrange form, or of firstorder equations in Hamilton form. According to the old idea due to S. Lie, ..."
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, and recently reconsidered by various authors (see e.g. [18] and references therein, see also e.g. [911] for more specific applications to dynamical problems), one may introduce the very general notion of Lie point symmetry
On Lie point symmetries in differential games
"... A technique to determine closedloop Nash equilibria of nplayer differential games is developed when their dynamic statecontrol system is composed of decoupled ODEs. In particular, the theory of Lie point symmetries is exploited to achieve first integrals of such systems. JEL Classification: C72, ..."
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A technique to determine closedloop Nash equilibria of nplayer differential games is developed when their dynamic statecontrol system is composed of decoupled ODEs. In particular, the theory of Lie point symmetries is exploited to achieve first integrals of such systems. JEL Classification: C72
Note on Lie point symmetries of Burgers Equations’
"... Abstract: In this work we study the Lie point symmetries of a class of evolution equations and obtain a group classification of these equations. We also identify the classical Lie algebras that the symmetry Lie algebras are isomorphic to. ..."
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Abstract: In this work we study the Lie point symmetries of a class of evolution equations and obtain a group classification of these equations. We also identify the classical Lie algebras that the symmetry Lie algebras are isomorphic to.
Lie Point Symmetries for Reduced Ermakov Systems
, 2008
"... Reduced Ermakov systems are defined as Ermakov systems restricted to the level surfaces of the Ermakov invariant. The condition for Lie point symmetries for reduced Ermakov systems is solved yielding four infinite families of systems. It is shown that SL(2,R) always is a group of point symmetries fo ..."
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Reduced Ermakov systems are defined as Ermakov systems restricted to the level surfaces of the Ermakov invariant. The condition for Lie point symmetries for reduced Ermakov systems is solved yielding four infinite families of systems. It is shown that SL(2,R) always is a group of point symmetries
Lie point symmetries of differentialdifference equations
 J. Phys. A Math.Theor
"... We present an algorithm for determining the Lie point symmetries of differential equations on fixed non transforming lattices, i.e. equations involving both continuous and discrete independent variables. The symmetries of a specific integrable discretization of the KricheverNovikov equation, the T ..."
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Cited by 2 (2 self)
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We present an algorithm for determining the Lie point symmetries of differential equations on fixed non transforming lattices, i.e. equations involving both continuous and discrete independent variables. The symmetries of a specific integrable discretization of the KricheverNovikov equation
Liepoint symmetries of the discrete Liouville equation
, 1407
"... The Liouville equation is well known to be linearizable by a point transformation. It has an infinite dimensional Lie point symmetry algebra isomorphic to a direct sum of two Virasoro algebras. We show that it is not possible to discretize the equation keeping the entire symmetry algebra as point sy ..."
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The Liouville equation is well known to be linearizable by a point transformation. It has an infinite dimensional Lie point symmetry algebra isomorphic to a direct sum of two Virasoro algebras. We show that it is not possible to discretize the equation keeping the entire symmetry algebra as point
Partial Liepoint symmetries of differential equations
 J. Phys. A: Math. Gen
"... When we consider a differential equation \Delta = 0 whose set of solutions is S, a Liepoint exact symmetry of this is a Liepoint invertible transformation T such that T (S) = S, i.e. such that any solution to \Delta = 0 is tranformed into a (generally, different) solution to the same equation; ..."
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Cited by 17 (11 self)
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When we consider a differential equation \Delta = 0 whose set of solutions is S, a Liepoint exact symmetry of this is a Liepoint invertible transformation T such that T (S) = S, i.e. such that any solution to \Delta = 0 is tranformed into a (generally, different) solution to the same equation
Lie Point Symmetries and Commuting Flows for Equations on Lattices
, 2008
"... Centre de recherches mathématiques and Département de mathématiques et de statistique, ..."
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Centre de recherches mathématiques and Département de mathématiques et de statistique,
Results 1  10
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