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

In this paper we study the splitting of separatrices phenomenon which ariseswhen one considers a Hamiltonian System of one degree of freedom with a fastperiodic or quasiperiodic and meromorphic in the state variables perturbation.The obtained results are different from the previous ones in the literature,which mainly assume algebraic or trigonometric polynomial dependence on thestate variables. As a model, we consider the pendulum equation with severalmeromorphic perturbations and we show the sensitivity of the size of thesplitting on the width of the analyticity strip of the perturbation withrespect to the state variables. We show that the size of the splitting isexponentially small if the strip of analyticity is wide enough. Furthermore, wesee that the splitting grows as the width of the analyticity strip shrinks,even becoming non-exponentially small for very narrow strips. Our resultsprevent from using polynomial truncations of the meromorphic perturbation tocompute the size of the splitting of separatrices.

Exponentially and non-exponentially small splitting of separatrices for the pendulum with a fast meromorphic perturbation