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(2004 / vol.7 / no.2)
Nonzero Lyapunov Exponents On Periodic Orbits Under Perturbations
Wenxiang Sun
Pages. 95-104     



Consider a $C^2$ vector field $S$ with a hyperbolic periodic orbit $Gamma$ that is not a singularity. Denote by $X^e(Gamma)$ the set of $C^2$ vector fields preserving the periodic orbit $Gamma$ together with its period. We construct an open neighborhood $U(S) subset X^2(Gamma)$ such that each vector field $X$ in $U(S)$ preserves all nonzero Lyapunov exponents with respect to $S$ on $Gamma$.



1. Introduction
2. Bundles and flows
3. Standard maps and essential perturbations
4. Proof of theorem 1.2
Refferences



Lyapunov exponent, periodic orbit, perturbation



37B38, 37D99