TAILIEUCHUNG - Đề tài " Ergodic properties of rational mappings with large topological degree "

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−n (f n )∗ Θ → µf for every smooth probability measure Θ on X. We show t 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 = dt µf. | Annals of Mathematics Ergodic properties of rational mappings with large topological degree By Vincent Guedj Annals of Mathematics 161 2005 1589 1607 Ergodic properties of rational mappings with large topological degree By Vincent Guedj Abstract Let X be a projective manifold and f X X a rational mapping with large topological degree dt xk-1 f the k 1 th dynamical degree of f. We give an elementary construction of a probability measure p f such that d-n fn 0 p-f for every smooth probability measure 0 on X. We show that every quasiplurisubharmonic function is p f-integrable. In particular ụ f does not charge either points of indeterminacy or pluripolar sets hence is f-invariant with constant jacobian f d f dt f. We then establish the main ergodic properties of p f it is mixing with positive Lyapunov exponents preimages of most points as well as repelling periodic points are equidistributed with respect to If. Moreover when dime X 3 or when X is complex homogeneous f is the unique measure of maximal entropy. Introduction Let X be a projective algebraic manifold and w a Hodge form on X normalized so that fx wk 1 k dime X. Let f X X be a rational mapping. We shall always assume in the sequel that f is dominating . its jacobian determinant does not vanish identically in any coordinate chart. We let If denote the indeterminacy locus of f the points where f is not holomorphic this is an algebraic subvariety of codimension 2. We let dt denote the topological degree of f this is the number of preimages of a generic point. Define f wk to be the trivial extension through If of f X If w A A f X If w. This is a Radon measure of total mass dt. When dt Ak-1 f see Section 1 below we give an elementary construction of a probability measure p f such that d-n fn wk p f. We show that every quasiplurisubharmonic function is f-integrable Theorem . In particular ụ f does not charge pluripolar sets. This answers a question raised by Russakovskii and Shiffman RS 97 which was .

TỪ KHÓA LIÊN QUAN
Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.