Bifurcations, intersections, and heights

Bifurcations, Intersections, and Heights

In this article, we prove the equivalence of dynamical stability, preperiodicity, and canonical height 0, for algebraic families of rational maps ft : P(C)→ P(C), parameterized by t in a quasi-projective complex variety. We use this to prove one implication in the if-and-only-if statement of [BD2, Conjecture 1.10] on unlikely intersections in the moduli space of rational maps; we present the co...

Deformations of maps on complete intersections, Damon’s KV -equivalence and bifurcations

A recent result of J. Damon’s [4] relates the Ae-versal unfoldings of a map-germ f with the KD(G)-versal unfoldings of an associated map germ which induces f from a stable map G. We extend this result to the case where the source is a complete intersection with an isolated singularity. In a similar vein, we also relate the bifurcation theoretic versal deformation of a bifurcation problem (map-g...

Heights and Weights

Tables of the relation between height and weight are now common in many countries, and if reasonably used are certainly helpful. It is not that a youth, a man, or woman, of a certain height must closely conform to the weight tabulated, a margin of 15 or 20 per cent, on either side is allowable. Such a table is undoubtedly useful in comparing the recruits or the prisoners it may be of one year (...

Fathers’ and daughters’ heights

Grazing Bifurcations and Chaos of a Hydraulic Engine Mount

The constitutive relationships of the rubber materials that act as the main spring of a hydraulic engine mount are nonlinear. In addition to material induced nonlinearity, further nonlinearities may be introduced by mount geometry, turbulent fluid behavior, temperature, boundary conditions, decoupler action, and hysteretic behavior. In this research all influence the behavior of the system only...