• Corpus ID: 238253067

Dynamically Stabilising Birational Surface Maps: Two Methods

@inproceedings{Birkett2021DynamicallySB,
  title={Dynamically Stabilising Birational Surface Maps: Two Methods},
  author={R. P. Birkett},
  year={2021}
}
We provide two new approaches to a theorem of Diller and Favre. Namely, a birational self-map f : X 99K X on a smooth projective surface X is birationally conjugate to a map which is algebraically stable. 

References

SHOWING 1-10 OF 12 REFERENCES
Degree Complexity of a Family of Birational Maps
We compute the degree complexity of a family of birational mappings of the plane with high order singularities.
Periodicities in linear fractional recurrences: Degree growth of birational surface maps
We consider the set of all 2-step recurrences (difference equations) that are given by linear fractional maps. These give birational maps of the plane. We determine the degree growth of these
Continuous families of rational surface automorphisms with positive entropy
For any k we construct k-parameter families of rational surface automorphisms with positive entropy. These are automorphisms of surfaces $${\mathcal{X}}$$, which are constructed from iterated blowups
Algebraic Geometry
Introduction to Algebraic Geometry.By Serge Lang. Pp. xi + 260. (Addison–Wesley: Reading, Massachusetts, 1972.)
Dynamics of Rational Surface Automorphisms: Linear Fractional Recurrences
We consider the family fa,b(x,y)=(y,(y+a)/(x+b)) of birational maps of the plane and the parameter values (a,b) for which fa,b gives an automorphism of a rational surface. In particular, we find
Do integrable mappings have the Painlevé property?
We present an integrability criterion for discrete-time systems that is the equivalent of the Painlev\'e property for systems of a continuous variable. It is based on the observation that for
Dynamics of bimeromorphic maps of surfaces
TLDR
It is shown that the sequence ║<i>f<sup>n</sup></i>*║ can be bounded, grow linearly, grow quadratically, or grow exponentially, and that after conjugating, f is an automorphism virtually isotopic to the identity, f preserves a rational fibration, or f preserves an elliptic fibration.
Linear Fractional Recurrences: Periodicities and Integrability
We consider k-step recurrences of the form $z_{n+k} = A(z)/B(z)$, where A and B are linear functions of $z_n, z_{n+1}, ..., z_{n+k-1}$, which we call k-step linear fractional recurrences. The first
MATH
TLDR
It is still unknown whether there are families of tight knots whose lengths grow faster than linearly with crossing numbers, but the largest power has been reduced to 3/z, and some other physical models of knots as flattened ropes or strips which exhibit similar length versus complexity power laws are surveyed.
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