منابع مشابه
Degree-growth of Monomial Maps
For projectivizations of rational maps Bellon and Viallet defined the notion of algebraic entropy using the exponential growth rate of the degrees of iterates. We want to call this notion to the attention of dynamicists by computing algebraic entropy for certain rationalmaps of projective spaces (Theorem6.2) and comparing it with topological entropy (Theorem 5.1). The particular rational maps w...
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We prove a formula for the multidegrees of a rational map defined by generalized monomials on a projective variety, in terms of integrals over an associated Newton region. This formula leads to an expression of the multidegrees as volumes of related polytopes, in the spirit of the classical Bernstein-Kouchnirenko theorem, but extending the scope of these formulas to more general monomial maps. ...
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One studies Cremona monomial maps by combinatorial means. Among the results is a simple integer matrix theoretic proof that the inverse of a Cremona monomial map is also defined by monomials of fixed degree, and moreover, the set of monomials defining the inverse can be obtained explicitly in terms of the initial data. A neat consequence is drawn for the plane Cremona monomial group, in particu...
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In this note, we study some of the simplest algebraic self-maps of projective spaces. These maps, which we call monomial maps, are in one-to-one correspondence with nonsingular integer matrices, and are closely related to toral endomorphisms. In Theorem 1 we give a lower bound for the topological entropy of monomial maps and in Theorem 2 we give a formula for algebraic entropy (as defined by Be...
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The arithmetic degree, the smallest extended degree, and the homological degree are invariants that have been proposed as alternatives of the degree of a module if this module is not Cohen-Macaulay. We compare these degree functions and study their behavior when passing to the generic initial or the lexicographic submodule. This leads to various bounds and to counterexamples to a conjecture of ...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2007
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385707000168