Birkhoff Normal Forms and KAM Theory for Gumowski-Mira Equation-Reference-Cited by-同舟云学术

Birkhoff Normal Forms and KAM Theory for Gumowski-Mira Equation

Published:2014 Issue: Volume:2014 Page:1-8
ISSN:2356-6140
Container-title:The Scientific World Journal
language:en
Short-container-title:The Scientific World Journal

Author:

Kulenović M. R. S.¹,Nurkanović Z.²,Pilav E.³

Affiliation:

1. Department of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USA

2. Department of Mathematics, University of Tuzla, 75000 Tuzla, Bosnia and Herzegovina

3. Department of Mathematics, University of Sarajevo, 71000 Sarajevo, Bosnia and Herzegovina

Abstract

By using the KAM theory we investigate the stability of equilibrium solutions of the Gumowski-Mira equation:xn+1=(2axn)/(1+xn2)-xn-1, n=0,1,…, wherex-1,x0∈(-∞,∞), and we obtain the Birkhoff normal forms for this equation for different equilibrium solutions.

Publisher

Hindawi Limited

Subject

General Environmental Science,General Biochemistry, Genetics and Molecular Biology,General Medicine

Link

http://downloads.hindawi.com/journals/tswj/2014/819290.pdf

Reference21 articles.

1. Lecture Notes in Mathematics,1980

2. On the algebraic difference equations un+2un = ψ(un+1) in , related to a family of elliptic quartics in the plane

3. On the algebraic difference equations un+2+un=ψ(un+1) in R, related to a family of elliptic quartics in the plane

4. Zeeman's Monotonicity Conjecture

5. DYNAMICS OF SOME RATIONAL DISCRETE DYNAMICAL SYSTEMS VIA INVARIANTS

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