Post-critically finite maps on ℙⁿ for

نویسندگان

چکیده

Let f : P n → f:{\mathbb P}^n\to {\mathbb P}^n be a morphism of degree alttext="d greater-than-or-equal-to 2"> d ≥ 0 encoding="application/x-tex">\ell \ge 0 such that the critical locus alttext="upper C r i t Subscript f"> Crit encoding="application/x-tex">\operatorname {Crit}_f satisfies k plus script left-parenthesis f right-parenthesis subset-of-or-equal-to right-parenthesis"> + stretchy="false">( stretchy="false">) ⊆<!-- ⊆ encoding="application/x-tex">f^{k+\ell }(\operatorname {Crit}_f)\subseteq {f^\ell (\operatorname {Crit}_f)} smallest l"> encoding="application/x-tex">\ell called tail-length. We prove for 3"> 3 3 alttext="n encoding="application/x-tex">n\ge , set PCF maps with tail-length at most alttext="2"> encoding="application/x-tex">2 not Zariski dense in parameter space all maps. In particular, periodic loci, i.e., equals = =0 are dense.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Inverse limit spaces of post - critically finite tent maps

Let (I, T ) be the inverse limit space of a post-critically finite tent map. Conditions are given under which these inverse limit spaces are pairwise nonhomeomorphic. This extends results of Barge & Diamond [2].

متن کامل

Critically Finite Maps and Attractors On

We first study the structure of the post-critical set of critically finite maps on P and show that the Julia set for a k−critically finite map is the whole of P. We then study a specific k−critically finite map and show that the only non-empty closed backward invariant subset is the whole of P . Based on this result, we give an example of a holomorphic map on P that has a chaotic nonalgebraic a...

متن کامل

The Fatou Set for Critically Finite Maps

It is a classical result in complex dynamics of one variable that the Fatou set for a critically finite map on P consists of only basins of attraction for superattracting periodic points. In this paper we deal with critically finite maps on P. We show that the Fatou set for a critically finite map on P consists of only basins of attraction for superattracting periodic points. We also show that ...

متن کامل

Heights on moduli space for post-critically finite dynamical systems

The purpose of this Research In Teams event was to consider the arithmetic properties of post-critically finite (PCF) rational maps. In the study of complex holomorphic dynamics, it is a general theme that the dynamical properties of a holomorphic map are largely determined by the behaviour of the critical points. In studying the dynamics of a rational map, then, one is lead to consider the orb...

متن کامل

ATTRACTING CYCLES IN p-ADIC DYNAMICS AND HEIGHT BOUNDS FOR POST-CRITICALLY FINITE MAPS

A rational function φ(z) of degree d ≥ 2 with coefficients in an algebraically closed field is post-critically finite (PCF) if all of its critical points have finite forward orbit under iteration. We show that the collection of PCF rational functions is a set of bounded height in the moduli space of rational functions over the complex numbers, once the well-understood family known as flexible L...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Transactions of the American Mathematical Society

سال: 2023

ISSN: ['2330-0000']

DOI: https://doi.org/10.1090/tran/8871