---
res:
  bibo_abstract:
  - We construct nontrivial deformations of the standard map which preserve the symplectic
    actions, respectively the Lyapunov exponents, of infinitely many periodic orbits
    accumulating to an invariant curve. The proof uses a resonant normal-form construction
    to obtain a sequence of periodic orbits accumulating on an invariant curve with
    a Liouville rotation number. Within these normal forms we capture the dependence
    of these periodic orbits on the resonant Fourier coefficients of the dynamics
    on the invariant curve and, using the contraction mapping principle, obtain a
    suitable deformation achieving the prescribed spectral data associated with this
    sequence of orbits. The result can be viewed as a symplectic twist-map analogue
    of a length spectral nonrigidity phenomenon for Riemannian manifolds and convex
    billiards, and it motivates the existence problem for similar 'partially length-isospectral'
    deformations of strictly convex billiard tables.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Yunzhe
      foaf_name: Li, Yunzhe
      foaf_surname: Li
      foaf_workInfoHomepage: http://www.librecat.org/personId=41cb05d3-f128-11eb-9611-e4e2b3cfba31
  bibo_doi: 10.48550/ARXIV.2512.03865
  dct_date: 2025^xs_gYear
  dct_language: eng
  dct_subject:
  - Dynamical Systems (math.DS)
  - 'FOS: Mathematics'
  - 'FOS: Mathematics'
  dct_title: Deformations of the standard map with prescribed actions and Lyapunov
    exponents@
...