PreprintCC0arXiv
Generic Linear Momentum Escape for Twist Maps
Abstract
We prove that linear momentum escape is generic in the C1,α topology for smooth potential perturbations of exact symplectic twist maps, for every 0<α<1. We assume a C2 generating function, a uniform twist condition, and uniform upper bounds on D11S and D22S. For an open dense set of potentials, every sufficiently small momentum drift is realized by an orbit. This genericity result does not extend in general to the C2 topology. We give examples with no nonzero linear drift under C2-small perturbations in every dimension. In dimension one, a second example has bounded momentum along every orbit under C2-small perturbations.
Related
- Persistence of invariant graphs for twist maps under analytic perturbations
- Foliations and minimality for twist maps
- Generic reconstruction of rational maps from multipliers of periods one and two
- Quantitative Persistence and Regularity of Invariant Graphs for Dissipative Twist Maps
- Isolated singularities of harmonic maps with generic boundary data
BibTeX
@misc{du2026generic,
title = {{Generic Linear Momentum Escape for Twist Maps}},
author = {Jianxing Du},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00254},
eprint = {2611.00254},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00254},
note = {CC0},
}
RIS
TY - UNPB
TI - Generic Linear Momentum Escape for Twist Maps
AU - Jianxing Du
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00254
UR - https://arxiv.org/abs/2611.00254
AB - We prove that linear momentum escape is generic in the C^1,α topology for smooth potential perturbations of exact symplectic twist maps, for every 0<α<1. We assume a C^2 generating function, a uniform twist condition, and uniform upper bounds on D_11S and D_22S. For an open dense set of potentials, every sufficiently small momentum drift is realized by an orbit. This genericity result does not extend in general to the C^2 topology. We give examples with no nonzero linear drift under C^2-small perturbations in every dimension. In dimension one, a second example has bounded momentum along every orbit under C^2-small perturbations.
ER -