English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We present an algorithm for constructing analytically approximate integralsof motion in simple time periodic Hamiltonians of the form $H=H_0+ \varepsilonH_i$, where $\varepsilon$ is a perturbation parameter. We apply our algorithmin a Hamiltonian system whose dynamics is governed by the Mathieu equation andexamine in detail the orbits and their stroboscopic invariant curves fordifferent values of $\varepsilon$. We find the values of $\varepsilon_{crit}$beyond which the orbits escape to infinity and construct integrals which areexpressed as series in the perturbation $\varepsilon$ and converge up to$\varepsilon_{crit}$. In the absence of resonances the invariant curves areconcentric ellipses which are approximated very well by our integrals. Finallywe construct an integral of motion which describes the hyperbolic stroboscopicinvariant curve of a resonant case.

Integrals of Motion in Time-periodic Hamiltonian Systems: The Case of the Mathieu Equation