2 problems

Zariski Dense Orbit conjecture for rational self-maps
arXiv@arxiv
Zariski Dense Orbit conjecture. If there is no non-constant rational function $g$ on $X$ satisfying $g\circ f=g$ , then $\mathcal{Z}(f)\neq\emptyset$ .
Conjectureopenarithmetic-dynamics dense-orbits rational-maps
1
Positive-characteristic dense-orbit conjecture over transcendental fields
arXiv@arxiv
Positive-characteristic dense-orbit conjecture. There exists a point $x\in X(k)$ whose orbit is Zariski dense in $X$ .
Conjectureopenalgebraic-dynamics dense-orbits positive-characteristic
0

Zariski Dense Orbit conjecture for rational self-maps