Gevrey Regularity of Invariant Curves of Analytic Reversible Mappings
<p/> <p>We prove the existence of a Gevrey family of invariant curves for analytic reversible mappings under weaker nondegeneracy condition. The index of the Gevrey smoothness of the family could be any number <inline-formula><graphic file="1687-1847-2010-324378-i1.gif"...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://www.advancesindifferenceequations.com/content/2010/324378 |
| Summary: | <p/> <p>We prove the existence of a Gevrey family of invariant curves for analytic reversible mappings under weaker nondegeneracy condition. The index of the Gevrey smoothness of the family could be any number <inline-formula><graphic file="1687-1847-2010-324378-i1.gif"/></inline-formula>, where <inline-formula><graphic file="1687-1847-2010-324378-i2.gif"/></inline-formula> is the exponent in the small divisors condition and <inline-formula><graphic file="1687-1847-2010-324378-i3.gif"/></inline-formula> is the order of degeneracy of the reversible mappings. Moreover, we obtain a Gevrey normal form of the reversible mappings in a neighborhood of the union of the invariant curves.</p> |
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| ISSN: | 1687-1839 1687-1847 |