Access the full text.
Sign up today, get DeepDyve free for 14 days.
Jurgen Poschel (2009)
A lecture on the classical KAM theoremarXiv: Dynamical Systems
M. Sevryuk (1995)
Kam-stable HamiltoniansJournal of Dynamical and Control Systems, 1
M. Herman (1992)
Twist Mappings and Their Applications
B. Fayad, R. Krikorian (2010)
Rigidity results for quasiperiodic SL(2, R) -cocyclesJournal of Modern Dynamics, 3
V. Zharnitsky (2000)
Invariant curve theorem for quasiperiodic twist mappings and stability of motion in the Fermi-Ulam problemNonlinearity, 13
Junxiang Xu, J. You (2007)
Gevrey-smoothness of invariant tori for analytic nearly integrable Hamiltonian systems under Rüssmann's non-degeneracy conditionJournal of Differential Equations, 235
G. Popov (2000)
Invariant Tori, Effective Stability, and Quasimodes with Exponentially Small Error Terms I –¶Birkhoff Normal FormsAnnales Henri Poincaré, 1
Xuemei Li, R. Llave (2010)
Convergence of differentiable functions on closed sets and remarks on the proofs of the "Converse Approximation Lemmas''Discrete and Continuous Dynamical Systems - Series S, 3
Dongfeng Zhang, Junxiang Xu (2006)
On elliptic lower dimensional tori for Gevrey-smooth Hamiltonian systems under Rüssmann's non-degeneracy conditionDiscrete and Continuous Dynamical Systems, 16
A. Delshams, R. Llave (2000)
KAM Theory and a Partial Justification of Greene's Criterion for Nontwist MapsSIAM J. Math. Anal., 31
(1981)
Demonstration du théorème des courbes translatées de nombre de rotation de type constant
J. Moser (1962)
On invariant curves of area-preserving mappings of an anulus
B. Fayad, R. Krikorian (2009)
Rigidity results for quasiperiodic SL ( 2 , R ) $\mathrm{SL}(2,R)$ -cocyclesJ. Mod. Dyn., 3
J. Moser (1967)
Convergent series expansions for quasi-periodic motionsMathematische Annalen, 169
A. Avila, B. Fayad, R. Krikorian (2010)
A KAM scheme for SL(2,R) cocycles with Liouvillean frequenciesarXiv: Dynamical Systems
C. Simó (1998)
Invariant curves of analytic perturbed nontwist area preserving maps
J. Bruna (1980)
An Extension Theorem of Whitney Type for Non Quasi‐Analytic Classes of FunctionsJournal of The London Mathematical Society-second Series, 22
B. Fayad, R. Krikorian (2009)
HERMAN'S LAST GEOMETRIC THEOREMAnnales Scientifiques De L Ecole Normale Superieure, 42
H. Whitney (1934)
Analytic Extensions of Differentiable Functions Defined in Closed SetsTransactions of the American Mathematical Society, 36
Dongfeng Zhang, Junxiang Xu (2006)
Gevrey-smoothness of elliptic lower-dimensional invariant tori in Hamiltonian systems under Rüssmann's non-degeneracy condition ✩Journal of Mathematical Analysis and Applications, 323
H. Rüssmann (1983)
Lecture Notes in Math.
D. del-Castillo-Negrete, J. Greene, P. Morrison (1997)
Renormalization and transition to chaos in area preserving nontwist mapsPhysica D: Nonlinear Phenomena, 100
J. Kovalevsky (1989)
Lectures in celestial mechanics
A. Avila, B. Fayad, R. Krikorian (2011)
A KAM scheme for SL ( 2 , R ) $\mathrm{SL}(2,R)$ cocycles with Liouvillean frequenciesGeom. Funct. Anal., 21
H. Rüssmann (1983)
On the existence of invariant curves of twist mappings of an annulus
R. Meise, Rüdiger Braun, José Solves, B. Taylor (1990)
Whitney's extension theorem for Non-Quasi-Analytic classes of ultradifferentiable functions, 5
F. Wagener (2003)
A note on Gevrey regular KAM theory and the inverse approximation lemmaDynamical Systems, 18
G. Popov (2003)
KAM theorem for Gevrey HamiltoniansErgodic Theory and Dynamical Systems, 24
H. Rüssmann (1976)
On a new proof of Moser's twist mapping theoremCelestial mechanics, 14
B. Fayad, K. Khanin (2006)
Smooth linearization of commuting circle diffeomorphismsAnnals of Mathematics, 170
M. Herman (1992)
Dynamics Connected with Indefinite Normal Torsion
Dongfeng Zhang, Rong Cheng (2010)
Gevrey Regularity of Invariant Curves of Analytic Reversible MappingsAdvances in Difference Equations, 2010
H. Broer, G. Huitema (1995)
Unfoldings of quasi-periodic tori in reversible systemsJournal of Dynamics and Differential Equations, 7
D. del-Castillo-Negrete, J. Greene, P. Morrison (1996)
Area preserving nontwist maps: periodic orbits and transition to chaosPhysica D: Nonlinear Phenomena, 91
In this paper we prove the existence of a Gevrey family of invariant curves for analytic area preserving mappings. The Gevrey smoothness is expressed by Gevrey index. We specifically obtain the Gevrey index of families of invariant curves which is related to the smoothness of area preserving mappings and the exponent of small divisors condition. Moreover, we obtain a Gevrey normal form of area preserving mappings in a neighborhood of the union of the invariant curves.
Acta Applicandae Mathematicae – Springer Journals
Published: Nov 9, 2017
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.