6 papers
Dynamical degrees of twisted rational maps
Marc Abboud, Junyi Xie
Twisted rational maps arise naturally in relative algebraic dynamics: if a rational self-map preserves a fibration, then the induced map on the generic fiber is usually not an ordi…
Recent progress on the geometric Bombieri--Lang conjecture
Junyi Xie
We survey recent progress on the geometric Bombieri--Lang conjecture over function fields of characteristic zero. We discuss recent work of Xie--Yuan and Guoquan Gao, which togethe…
Space spanned by characteristic exponents
Zhuchao Ji, Junyi Xie, Geng-Rui Zhang
We prove several rigidity results on multiplier spectrum and length spectrum. For example, we show that for every non-exceptional rational map $f:\mathbb{P}^1(\mathbb{C})\to\mathbb…
Local rigidity of Julia sets
Zhuchao Ji, Junyi Xie
We find criteria ensuring that a local (holomorphic, real analytic, ) homeomorphism between the Julia sets of two given rational functions comes from an algebraic corresponden…
Homoclinic orbits, multiplier spectrum and rigidity theorems in complex dynamics
Zhuchao Ji, Junyi Xie
The aims of this paper are to answer several conjectures and questions about multiplier spectrum of rational maps and to give new proofs of several rigidity theorems in complex dyn…
Birational conjugacies between endomorphisms on the projective plane
Serge Cantat, Junyi Xie
We proved that, in characteristic 0, if two dominant endomorphisms of the projective plane of degree at least 2 are conjugate by some birational transformation, then they are conju…