## Some dynamical properties of pseudo-automorphisms in dimension $3$

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- by Tuyen Trung Truong PDF
- Trans. Amer. Math. Soc.
**368**(2016), 727-753

## Abstract:

Let $X$ be a compact Kähler manifold of dimension $3$ and let $f:X\rightarrow X$ be a pseudo-automorphism. Under the mild condition that $\lambda _1(f)^2>\lambda _2(f)$, we prove the existence of invariant positive closed $(1,1)$ and $(2,2)$ currents, and we also discuss the (still open) problem of intersection of such currents. We prove a weak equi-distribution result for Green $(1,1)$ currents of meromorphic selfmaps, not necessarily algebraic $1$-stable, of a compact Kähler manifold of arbitrary dimension and discuss how a stronger equidistribution result may be proved for pseudo-automorphisms in dimension $3$. As a byproduct, we show that the intersection of some dynamically related currents is well-defined with respect to our definition here, even though not obviously to be seen so using the usual criteria.## References

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## Additional Information

**Tuyen Trung Truong**- Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244
- Address at time of publication: School of Mathematics, Korea Institute for Advanced Study, Seoul 130-722, Republic of Korea
- MR Author ID: 724811
- Email: tutruong@syr.edu, truong@kias.re.kr
- Received by editor(s): May 8, 2013
- Received by editor(s) in revised form: December 3, 2013
- Published electronically: December 16, 2014
- © Copyright 2014 by the author
- Journal: Trans. Amer. Math. Soc.
**368**(2016), 727-753 - MSC (2010): Primary 37F99, 32H50
- DOI: https://doi.org/10.1090/S0002-9947-2014-06340-X
- MathSciNet review: 3413882