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In many cases rational surfaces obtained by desingularization of birational dynamical systems are not relatively minimal. We propose a method to obtain coordinates of relatively minimal rational surfaces by using blowing down structure. We apply this method to the study of various integrable or linearizable mappings, including discre
We prove that the natural $(operatorname{Aff} _2(mathbf{C}),mathbf{C}^2)$-structure on an Inoue surface is the unique $(operatorname{Bir}(mathbb{P}^2),mathbb{P}^2(mathbf{C}))$-structure, generalizing a result of Bruno Klingler which asserts that the
We show how singularities shape the evolution of rational discrete dynamical systems. The stabilisation of the form of the iterates suggests a description providing among other things generalised Hirota form, exact evaluation of the algebraic entropy
Toric dynamical systems are known as complex balancing mass action systems in the mathematical chemistry literature, where many of their remarkable properties have been established. They include as special cases all deficiency zero systems and all de
Fix a symplectic K3 surface X homologically mirror to an algebraic K3 surface Y by an equivalence taking a graded Lagrangian torus L in X to the skyscraper sheaf of a point y of Y. We show there are Lagrangian tori with vanishing Maslov class in X wh
We describe the set of all $(3,1)$-rational functions given on the set of complex $p$-adic field $mathbb C_p$ and having a unique fixed point. We study $p$-adic dynamical systems generated by such $(3,1)$-rational functions and show that the fixed po