Convex and toric geometry to analyze complex dynamics in chemical reaction systems

DISSERTATION zur Erlangung des akademischen Grades doctor rerum naturalium Dedicated to the memory of KARIN GATERMANN Table 1: List of mathematical symbols C field of complex numbers R field of real numbers Z ring of integer numbers C[x] ring of polynomials with coefficients in the field of complex numbers I ideal I def, tor deformed toric ideal V (I) variety of an ideal V (I def, tor) variety of a deformed toric variety F h, j family of polynomials depending on the parameters h, j F P N family of polynomials with a certain sign pattern in the coefficients D A family of all matrices emerging from the matrix A if it is multiplied by a positive definite diagonal matrix S A family of all matrices having the same sign pattern as the matrix A N stoichiometric matrix ν ij stoichiometric coefficient of the i t h-species in the j th