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J. (1981). AUTO : A program for the automatic bifurcation analysis of autonomous systems. Congressus Numerantium 30, 265-284. , Stewart, I. G. (1988). Singularities and Groups in Bifurcation Theory, Vol. II. Appl. Math. Sci. 69, Springer, New York. su Smooth hamiltonian vectorfieldswith linear symmetries and anti-symmetries are considered. We prove that provided symmetry group is compact then a smooth conjugacy in Stemberg-Chen Theorem can be chosen canonical and symmetric. Introduction The well-known Sternberg Theorem (see *) asserts that if two local smooth vector fields are formally conjugate at a hyperbolic singularity then they are smoothly conjugate.
Since the phase flows P* and <2* commute then Q ' ^ P ' 1 ^ ) ) = (qt2(ptl(x,e),e (l + t1),e + t1) 9 = (P («* (^e)»e)»£ + *i) = P ' H Q ' 2 (*,£)), or g* 2 (p tl (x ) e),e + t i ) = p t l ( 9 t 2 ( ^ £ ) , e ) - 23 For e = 0, ti = 1, *2 = * this gives « V ( * , 0 ) , 1 ) =P X (**(*, 0),0). , G is a conjugacy between £ and 77. Condition (1) is equivalent to the equation Di
Bridges and G. Derks. Unstable eigenvalues, and the linearisation about solitary waves and fronts with symmetry. Proc. Roy. Soc. Lond. A, 455:2427-2469,1999. 8. J. Bridges and G. Derks. The symplectic Evans matrix, and the instability of solitary waves and fronts. Arch. Rat. Mech. , 156:1-87, 2001. 9. J. Bridges and G. Derks. Linear instability of solitary wave solutions of the Kawahara equation and its generalisations. Submitted. 10. W. Evans. Nerve axon equations, IV: The stable and unstable impulse.