| Abstract: |
| We present an algorithm to compute an invariant circle and the corresponding
isochrons for 2-dimensional maps. The algorithm is based on solving an
invariance equation using a quasi-Newton method. We prove that the algorithm
converges super-exponentially if the initial guess satisfies the invariance
equation very approximately. This algorithm works irrespective of whether the
dynamics on the invariant circle is a rotation or it is phase-locked. It is also numerically efficient since the operation count per step is very small and the memory requirements are small (no matrices of data are stored). The main theorem is in an a-posteriori format and can lead to computer-assisted proofs. |
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