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## Invariance and first integrals of continuous and discrete Hamiltonian equations

- V. Dorodnitsyn, R. Kozlov
- Mathematics
- 10 June 2009

The relation between symmetries and first integrals for both continuous canonical Hamiltonian equations and discrete Hamiltonian equations is considered. The observation that canonical Hamiltonian… Expand

## Symmetries of systems of stochastic differential equations with diffusion matrices of full rank

- R. Kozlov
- Mathematics
- 18 June 2010

Lie point symmetries of a system of stochastic differential equations (SDEs) with diffusion matrices of full rank are considered. It is proved that the maximal dimension of a symmetry group admitted… Expand

## On maximal Lie point symmetry groups admitted by scalar stochastic differential equations

- R. Kozlov
- Mathematics
- 20 May 2011

It is proved that the Lie point symmetry group admitted by a scalar stochastic differential equation (SDE) of order n ⩾ 3 is at most (n + 2) dimensional. This result supplements those for first- and… Expand

## The group classification of a scalar stochastic differential equation

- R. Kozlov
- Mathematics
- 12 January 2010

Lie point group classification of a scalar stochastic differential equation (SDE) with one-dimensional Brownian motion is presented. The admitted symmetry group can be zero, one, two or three… Expand

## Continuous symmetries of Lagrangians and exact solutions of discrete equations

- V. Dorodnitsyn, R. Kozlov, P. Winternitz
- Mathematics
- 23 July 2003

One of the difficulties encountered when studying physical theories in discrete space–time is that of describing the underlying continuous symmetries (like Lorentz, or Galilei invariance). One of the… Expand

## The Whole Set of Symmetry Preserving Discrete Versions of a Heat Transfer Equation with a Source. 1

- V. Dorodnitsyn, R. Kozlov
- Mathematics
- 1997

In this letter we present the set of invariant di erence equations and meshes which preserve the Lie group symmetries of the equation ut = (K(u)ux)x +Q(u): All special cases of K(u) and Q(u) that… Expand

## Conservative discretizations of the Kepler motion

- R. Kozlov
- Physics
- 27 April 2007

Modified vector fields are used to construct high-order conservative discretizations of the three-dimensional Kepler motion. The numerical integrators preserve the Hamiltonian function, the angular… Expand

## Symmetry-preserving difference schemes for some heat transfer equations

- M. Bakirova, V. Dorodnitsyn, R. Kozlov
- Mathematics, Computer Science
- 7 December 1997

## First integrals of difference Hamiltonian equations

- V. Dorodnitsyn, R. Kozlov
- Mathematics, Physics
- 27 October 2009

In the present paper, the well-known Noether's identity, which represents the connection between symmetries and first integrals of Euler–Lagrange equations, is rewritten in terms of the Hamiltonian… Expand

## A Heat Transfer with a Source: the Complete Set of Invariant Difference Schemes

- V. Dorodnitsyn, R. Kozlov
- Mathematics, Physics
- 1 January 2003

Abstract In this letter we present the set of invariant difference equations and meshes which preserve the Lie group symmetries of the equation u t=(K(u)u x)x + Q(u). All special cases of K(u) and… Expand

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