High-precision continuation of periodic orbits. (English) Zbl 1248.65130
Summary: Obtaining periodic orbits of dynamical systems is the main source of information about how the orbits, in general, are organized. In this paper, we extend classical continuation algorithms in order to be able to obtain families of periodic orbits with high-precision. These periodic orbits can be corrected to get them with arbitrary precision. We illustrate the method with two important classical Hamiltonian problems.
MSC:
| 65P10 | Numerical methods for Hamiltonian systems including symplectic integrators |
| 37C27 | Periodic orbits of vector fields and flows |
| 37M15 | Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems |
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