Attracted by an elliptic fixed point
Bassam Fayad (IMJ-PRG), Jean-Pierre Marco (UPMC), David Sauzin, (IMCCE), J.-P Marco
TL;DR
This paper presents examples of symplectic diffeomorphisms in six-dimensional space where a non-resonant elliptic fixed point attracts orbits, challenging typical stability expectations.
Contribution
It provides explicit examples of symplectic maps with attracting elliptic fixed points, a phenomenon rarely demonstrated in higher dimensions.
Findings
Existence of attracting elliptic fixed points in symplectic diffeomorphisms.
Explicit construction of such examples in R^6.
Implications for stability theory in Hamiltonian dynamics.
Abstract
We give examples of symplectic diffeomorphisms of R^6 for which the origin is a non-resonant elliptic fixed point which attracts an orbit.
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