B R Sitaram
Articles written in Pramana – Journal of Physics
Volume 23 Issue 4 October 1984 pp 459-465 Mathematical Physics
Quasi invariants and generalized killing vectors
The connection between quasi-invariants (invariants of a Hamiltonian system defined only on a single constant energy hypersurface) and generalized Killing vector fields associated with the corresponding Jacobi metric is investigated. The results are used to deduce a generalised form of the classical Whittaker problem in two degrees of freedom.
Volume 27 Issue 3 September 1986 pp 363-370 Mathematical Physics
Quasi-invariants and generalized Killing vectors-II
We consider here the problem of the existence of a quasi-invariant which is linear in the momenta for Hamiltonians in three degrees of freedom. We show that such quasi-invariants are more constrained in their structure than in the two degrees of freedom case. We also show that some of these quasi-invariants have to be interpreted as ‘pseudo-translations’, i.e., as translations in a non-orthogonal system of coordinates.
Volume 44 Issue 4 April 1995 pp 295-302
Invariants of chaotic Hamiltonian systems
The invariants of chaotic bounded Hamiltonian systems and their relation to the solutions of the first variational equations of the equations of motion are studied. We show that these invariants are characterized by the fact that they either lose the property of differentiability as functions on phase space or that a certain formal power series defined in terms of the derivatives of the invariants has zero radius of convergence. For a specific example, we show that the former possibility appears to apply.
Volume 45 Issue 2 August 1995 pp 141-148
Time dependent canonical perturbation theory I: General theory
In this communication, we reanalyze the causes of the singularities of canonical perturbation theory and show that some of these singularities can be removed by using time-dependent canonical perturbation theory. A study of the local and global properties (in terms of the perturbation parameter) is also undertaken.
Volume 45 Issue 2 August 1995 pp 149-164
Time dependent canonical perturbation theory II: Application to the Henon-Heiles system
In this communication, we report the results of the application of time-dependent perturbation theory to the Henon-Heiles system. We show that the predictions of the perturbation theory hold good for short times, and try to explain the increase of error in the predicted results with the increase in energy.
Volume 46 Issue 5 May 1996 pp 323-329
Time dependent canonical perturbation theory III: Application to a system with nonconstant unperturbed frequencies
In this communication, we report the results of the application of time dependent perturbation theory to a non-integrable Hamiltonian which is a perturbation on a Hamiltonian with nonconstant frequencies. The theory provides good time dependent local constants of motion and also gives good approximation for mapping of solutions for a time limit determined by the nearest singularity in complex
Volume 49 Issue 2 August 1997 pp 193-197 Research Articles
Differentiability of invariants and Liapunov equations in Hamiltonian systems
In this communication, we investigate the behavior of the derivatives of invariants for Hamiltonian systems, using information derived from an analysis of the Liapunov exponents of the system. We show that under certain conditions on the analyticity properties of the solutions of the equations of motion, it is possible to construct 2
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