The Existence of Analytic Invariant Curves for a Planar Map

Ling Xia Liu

doi:10.4028/www.scientific.net/AMR.225-226.1274

Paper Titles

Prediction of Soil TN and TC at a Farm-Scale Using VIS-NIR Spectroscopy
p.1258

The Application of Red Mud on Restoring Heavy Metal Contaminated Water and Soil
p.1262

Study on Improved Genetic Algorithm for Min-Max Vehicle Routing Problem
p.1266

Stability Criterion of Discrete Hopfield Neural Networks with Multiple Delays in Parallel Mode: Linear Matrix Inequality
p.1270

The Existence of Analytic Invariant Curves for a Planar Map
p.1274

A Solution Method for Engineering Equilibrium Mathematics Modeling under Mild Conditions
p.1279

The Study of New Trend for DSC Scene Effects Technology
p.1284

Teaching System Construction and Optimization of Environmental Monitoring
p.1288

Research on the Entity Relation Extraction of Field Based on Semi-Supervised
p.1292

HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 225-226The Existence of Analytic Invariant Curves for a...

The Existence of Analytic Invariant Curves for a Planar Map

Abstract:

In this paper, we study the existence of analytic invariant curves for two-dimensional maps in the complex field C. Employing the method of majorant series, we discuss the eigenvalueof the mapping at a fixed point. We discuss not only thoseat resonance, i.e., at a root of the unity but also thosenear resonance under Brjuno condition.

You might also be interested in these eBooks

Advanced Research on Automation, Communication, Architectonics and Materials

View Preview

Info:

Periodical:

Advanced Materials Research (Volumes 225-226)

Pages:

1274-1278

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.225-226.1274

Citation:

Cite this paper

Online since:

April 2011

Authors:

Ling Xia Liu

Keywords:

Brjuno Condition, Invariant Curves, Planar Map, Resonance

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

References

[1] E. Fontich, Transversal homoclinic points of a class of conservative diffeomorphisms. J. Differential Equations, vol. 87, pp.1-12 (1990).

DOI: 10.1016/0022-0396(90)90012-e

Google Scholar

[2] J. Moser, The analytic invariants of an area-preserving mapping near a hyperbolic fix point. Comm. Pure Appl. Math.，vol. 9, pp.673-692 (1956).

DOI: 10.1002/cpa.3160090404

Google Scholar

[3] J. Moser, On invariant curves of area-preserving maps of an annulus. Nachr. Akad. Wiss. Gottingen，vol. 1, pp.199-226 (1962).

Google Scholar

[4] P. M. Diamond, Analytic invariants of mappings of two variables. J. Math. Anal. Appl., vol. 27, pp.601-608 (1969).

Google Scholar

[5] W. R. Li, S. S. Cheng, Analytic solutions of an iterative functional equations, Aequationes Math., vol. 68, pp.21-27 (2004).

Google Scholar

[6] A. D. Bjuno, Analytic form of differential equations. Trans. Moscow Math. Soc., vol. 25, pp.131-288 (1971).

Google Scholar

[7] S. Marmi, P. Moussa and J.-C. Yoccoz, The Brjuno functions and their regularity properties. Comm. Math. Phys., vol. 186, no. 2, pp.265-293 (1997).

DOI: 10.1007/s002200050110

Google Scholar

[8] M. S. Berger, "Nonlinearity and Functional Analysis", Academic Press (1977).

Google Scholar

[9] C.L. Siegel, "Vorlesungenuber Himmelsmechanik," Springer-Verlag: Berlin (1956).

Google Scholar

[10] T. Carletti and S. Marmi, Linearization of Analytic and Non-Analytic Germs of Diffeomorphisms of (C, 0). Bull. Soc. Math., France, vol. 128, pp.69-85 (2000).

DOI: 10.24033/bsmf.2363

Google Scholar

[11] A. M. Davie, The critical function for the semistandard map. Nonlinearity, vol. 7, pp.219-229 (1994).

DOI: 10.1088/0951-7715/7/1/009

Google Scholar