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Pull-back of currents by meromorphic maps

Tuyen Trung Truong (2013)

Bulletin de la Société Mathématique de France

Let  X and Y be compact Kähler manifolds, and let  f : X → Y be a dominant meromorphic map. Based upon a regularization theorem of Dinh and Sibony for DSH currents, we define a pullback operator f ♯ for currents of bidegrees ( p , p ) of finite order on  Y (and thus foranycurrent, since Y is compact). This operator has good properties as may be expected. Our definition and results are compatible to those of various previous works of Meo, Russakovskii and Shiffman, Alessandrini and Bassanelli, Dinh and Sibony, and can...

Pulling back cohomology classes and dynamical degrees of monomial maps

Jan-Li Lin (2012)

Bulletin de la Société Mathématique de France

We study the pullback maps on cohomology groups for equivariant rational maps (i.e., monomial maps) on toric varieties. Our method is based on the intersection theory on toric varieties. We use the method to determine the dynamical degrees of monomial maps and compute the degrees of the Cremona involution.

Puzzles of Quasi-Finite Type, Zeta Functions and Symbolic Dynamics for Multi-Dimensional Maps

Jérôme Buzzi (2010)

Annales de l’institut Fourier

Entropy-expanding transformations define a class of smooth dynamics generalizing interval maps with positive entropy and expanding maps. In this work, we build a symbolic representation of those dynamics in terms of puzzles (in Yoccoz’s sense), thus avoiding a connectedness condition, hard to satisfy in higher dimensions. Those puzzles are controled by a «constraint entropy» bounded by the hypersurface entropy of the aforementioned transformations.The analysis of those puzzles rests on a «stably...

Quantitative recurrence in two-dimensional extended processes

Françoise Pène, Benoît Saussol (2009)

Annales de l'I.H.P. Probabilités et statistiques

Under some mild condition, a random walk in the plane is recurrent. In particular each trajectory is dense, and a natural question is how much time one needs to approach a given small neighbourhood of the origin. We address this question in the case of some extended dynamical systems similar to planar random walks, including ℤ2-extension of mixing subshifts of finite type. We define a pointwise recurrence rate and relate it to the dimension of the process, and establish a result of convergence in...

Quantization Dimension Function and Ergodic Measure with Bounded Distortion

Mrinal Kanti Roychowdhury (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

The quantization dimension function for the image measure of a shift-invariant ergodic measure with bounded distortion on a self-conformal set is determined, and its relationship to the temperature function of the thermodynamic formalism arising in multifractal analysis is established.

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