Ergodic properties of rational mappings with large topological degree | Annals of Mathematics

Abstract Let X be a projective manifold and f:X→X a rational mapping with large topological degree, dt>λk−1(f):= the (k−1)th dynamical degree of f. We give an elementary construction of a probability measure μf such that d−nt(fn)∗Θ→μf for every smooth probability measure Θ on X. We show that every quasiplurisubharmonic function is μf-integrable. In particular μf does not charge either points of indeterminacy or pluripolar sets, hence μf is f-invariant with constant jacobian f∗μf=dtμf. We then establish the main ergodic properties of μf: it is mixing with positive Lyapunov exponents, preimages of “most” points as well as repelling periodic points are equidistributed with respect to μf. Moreover, when dimℂX≤3 or when X is complex homogeneous, μf is the unique measure of maximal entropy.

KEYWORDS

SHARE & LIKE

COMMENTS

ABOUT THE AUTHOR

数学年刊(Annals of Mathematics)

0 Following 0 Fans 0 Projects 674 Articles

SIMILAR ARTICLES

Abstract For any nondegenerate, quasi-homogeneous hypersurface singularity, we describe a family of moduli spaces, a virtual cycle, and a correspondin

阅读更多

Abstract For a large class of nonlinear Schrödinger equations with nonzero conditions at infinity and for any speed c less than the sound velocity, we

阅读更多

Abstract Let L2,p(ℝ2) be the Sobolev space of real-valued functions on the plane whose Hessian belongs to Lp. For any finite subset E⊂ℝ2 and p>2, let

阅读更多

Abstract We prove that for any group G in a fairly large class of generalized wreath product groups, the associated von Neumann algebra LG completely

阅读更多

Abstract We study the parity of 2-Selmer ranks in the family of quadratic twists of an arbitrary elliptic curve E over an arbitrary number field K. We

阅读更多

Abstract This paper has two main results. Firstly, we complete the parametrisation of all p-blocks of finite quasi-simple groups by finding the so-cal

阅读更多

Abstract We derive sharp Moser-Trudinger inequalities on the CR sphere. The first type is in the Adams form, for powers of the sublaplacian and for ge

阅读更多

Abstract We prove that isoparametric hypersurfaces with (g,m)=(6,2) are homogeneous, which answers Dorfmeister-Neher’s conjecture affirmatively and so

阅读更多

Abstract We prove the periodicity conjecture for pairs of Dynkin diagrams using Fomin-Zelevinsky’s cluster algebras and their (additive) categorificat

阅读更多

Abstract If F(x,y)∈ℤ[x,y] is an irreducible binary form of degree k≥3, then a theorem of Darmon and Granville implies that the generalized superellipt

阅读更多