Perturbations of symmetric elliptic Hamiltonians of degree four |
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Authors: | Chengzhi Li Pavao Mardeši? |
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Institution: | a LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, PR China b Institut de Mathématique de Bourgogne, U.M.R. 5584 du C.N.R.S., Université de Bourgogne, B.P. 47 870, 21078 Dijon Cedex, France |
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Abstract: | In this paper four-parameter unfoldings Xλ of symmetric elliptic Hamiltonians of degree four are studied. We prove that in a compact region of the period annulus of X0 the displacement function of Xλ is sign equivalent to its principal part, which is given by a family induced by a Chebychev system; and we describe the bifurcation diagram of Xλ in a full neighborhood of the origin in the parameter space, where at most two limit cycles can exist for the corresponding systems. |
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Keywords: | 34C07 34C08 37G15 |
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