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Invariant curves and boundedness of solutions of a class of reversible systems
Author(s) -
Yang Xiaojing,
Lo Kueiming
Publication year - 2009
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510727
Subject(s) - mathematics , bounded function , symplectic geometry , invariant (physics) , pure mathematics , planar , class (philosophy) , mathematical analysis , combinatorics , mathematical physics , computer graphics (images) , artificial intelligence , computer science
In this paper, the boundedness of all solutions for the following planar reversible system Ju ′ = ∇ H ( u ) + G ( u ) + h ( t ) is discussed, where the function H ( u ) ∈ C 2 (ℝ 2 , ℝ + ) is positive for u ≠ 0 and positively ( q , p )‐quasihomogeneous of quasi‐degree pq , G ∈ C 5 is bounded, h ∈ C 6 is 2 π ‐periodic and J is the standard symplectic matrix. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)