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2013
Impact Factor

Tan Su

UK, LE11 3TU
Department of Mathematical Sciences, Loughborough University

Publications:

Neishtadt A. I., Su T.
On Phenomenon of Scattering on Resonances Associated with Discretisation of Systems with Fast Rotating Phase
2012, vol. 17, no. 3-4, pp.  359-366
Abstract
Numerical integration of ODEs by standard numerical methods reduces continuous time problems to discrete time problems. Discrete time problems have intrinsic properties that are absent in continuous time problems. As a result, numerical solution of an ODE may demonstrate dynamical phenomena that are absent in the original ODE. We show that numerical integration of systems with one fast rotating phase leads to a situation of such kind: numerical solution demonstrates phenomenon of scattering on resonances that is absent in the original system.
Keywords: systems with rotating phases, passage through a resonance, numerical integration, discretisation
Citation: Neishtadt A. I., Su T.,  On Phenomenon of Scattering on Resonances Associated with Discretisation of Systems with Fast Rotating Phase, Regular and Chaotic Dynamics, 2012, vol. 17, no. 3-4, pp. 359-366
DOI:10.1134/S1560354712030100
Su T.
On the Accuracy of Conservation of Adiabatic Invariants in Slow-Fast Hamiltonian Systems
2012, vol. 17, no. 1, pp.  54-62
Abstract
Let the adiabatic invariant of action variable in a slow-fast Hamiltonian system with two degrees of freedom have limits along the trajectories as time tends to plus and minus infinity. The difference of these two limits is exponentially small in analytic systems. An isoenergetic reduction and canonical transformations are applied to transform the slow-fast system to form of a system depending on a slowly varying parameter in a complexified phase space. On the basis of this method an estimate for the accuracy of conservation of adiabatic invariant is given.
Keywords: adiabatic invariant, slow-fast Hamiltonian systems, isoenergetic reduction
Citation: Su T.,  On the Accuracy of Conservation of Adiabatic Invariants in Slow-Fast Hamiltonian Systems, Regular and Chaotic Dynamics, 2012, vol. 17, no. 1, pp. 54-62
DOI:10.1134/S1560354712010054

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