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  • PetscheClaytonMathematicsCriticallySeparableRational(VOR).pdf

    Creator:
    Petsche, Clayton
    Abstract:
    Given a number field K, we consider families of critically separable rational maps of degree d over K possessing a certain fixed-point and multiplier structure. With suitable notions of isomorphism and good reduction between rational maps in these families, we prove a finiteness theorem which is analogous to Shafarevich’s theorem...

  • PetscheClaytonMathematicsCriticallySeparableRational(AM).pdf

    Creator:
    Petsche, Clayton
    Abstract:
    Given a number field K, we consider families of critically separable rational maps of degree d over K possessing a certain fixed-point and multiplier structure. With suitable notions of isomorphism and good reduction between rational maps in these families, we prove a finiteness theorem which is analogous to Shafarevich’s theorem...

  • On the distribution of orbits in affine varieties

    Creator:
    Petsche, Clayton
    Abstract:
    Given an affine variety X, a morphism ϕ:X→X, a point α∈X, and a Zariski-closed subset V of X, we show that the forward ϕ-orbit of α meets V in at most finitely many infinite arithmetic progressions, and the remaining points lie in a set of Banach density zero. This may...
    Resource Type:
    Article

  • Critically Separable Rational Maps in Families

    Creator:
    Petsche, Clayton
    Abstract:
    Given a number field K, we consider families of critically separable rational maps of degree d over K possessing a certain fixed-point and multiplier structure. With suitable notions of isomorphism and good reduction between rational maps in these families, we prove a finiteness theorem which is analogous to Shafarevich’s theorem...
    Resource Type:
    Article

  • A dynamical pairing between two rational maps

    Creator:
    Petsche, Clayton, Szpiro, Lucien, and Tucker, Thomas J.
    Abstract:
    Given two rational maps φ and ψ on Ρ¹ of degree at least two, we study a symmetric, nonnegative real-valued pairing〈φ, ψ〉which is closely related to the canonical height functions hφ and hψ associated to these maps. Our main results show a strong connection between the value of〈φ, ψ〉and the...
    Resource Type:
    Article