On exact discretization of cubic-quintic Duffing oscillator. (English) Zbl 1396.37064
The author applies intersection theory to construct \(n\)-point finite-difference equations associated with classical integrable systems. As an example, a few exact discretizations of one-dimensional cubic and quintic Duffing oscillators sharing the form of the Hamiltonian and canonical Poisson bracket up to the integer scaling factor are presented.
Reviewer: Eszter Gselmann (Debrecen)
MSC:
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 37J05 | Relations of dynamical systems with symplectic geometry and topology (MSC2010) |
| 70K30 | Nonlinear resonances for nonlinear problems in mechanics |
| 70H05 | Hamilton’s equations |
| 39A12 | Discrete version of topics in analysis |
| 39A21 | Oscillation theory for difference equations |
Keywords:
Duffing oscillator; exact discretization; intersection theory; generalized oscillator with cubic non-linearity; cubic-quintic Duffing oscillatorSoftware:
Book3264ExamplesReferences:
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