Remarks on iterated cubic maps.
Milnor, John (1992)
Experimental Mathematics
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Displaying similar documents to “A family of cubic rational maps and matings of cubic polynomials.”
Remarks on iterated cubic maps.
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One considers representation of cubic polynomials in several variables as the sum of values of univariate polynomials taken at linear combinations of the variables.
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Let ϵ be a totally real cubic algebraic unit. Assume that the cubic number field ℚ(ϵ) is Galois. Let ϵ, ϵ' and ϵ'' be the three real conjugates of ϵ. We tackle the problem of whether {ϵ,ϵ'} is a system of fundamental units of the cubic order ℤ[ϵ,ϵ',ϵ'']. Given two units of a totally real cubic order, we explain how one can prove that they form a system of fundamental units of this order. Several explicit families of totally real cubic orders defined by parametrized families of cubic...
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We resolve the centre-focus problem for a specific class of cubic systems and determine the number of limit cycles which can bifurcate from a fine focus. We also describe the methods which we have developed to investigate these questions in general. These involve extensive use of Computer Algebra; we have chosen to use REDUCE.