43 citations · 239 across the 66 of their papers we have counts for
21 papers · 1 filter
Standard conjecture D and some conjectures around Weil's Riemann hypothesis
Tuyen Trung Truong
Let be a smooth projective variety defined on a finite field . On there is a special morphism , which raises coordinates to exponent : …
Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves
John Erik Fornæss, Mi Hu, Tuyen Trung Truong
In this paper, we research more in depth properties of Backtracking New Q-Newton's method (recently designed by the third author), when used to find roots of meromorphic functions.…
The Riemann hypothesis and dynamics of Backtracking New Q-Newton's method
Thuan Quang Tran, Tuyen Trung Truong
A new variant of Newton's method - named Backtracking New Q-Newton's method (BNQN) - was recently introduced by the second author. This method has good global convergence guarantee…
Backtracking New Q-Newton's method, Schröder's theorem, and Linear Conjugacy
John Erik Fornaess, Mi Hu, Tuyen Trung Truong +1
A new variant of Newton's method - named Backtracking New Q-Newton's method (BNQN) - which has strong theoretical guarantee, is easy to implement, and has good experimental perform…
Topological entropy of a rational map over a complete metrized field
Charles Favre, Tuyen Trung Truong, Junyi Xie
We prove that the topological entropy of any dominant rational self-map of a projective variety defined over a complete non-Archimedean field is bounded from above by the maximum o…
Strong submeasures and applications to non-compact dynamical systems
Tuyen Trung Truong
A strong submeasure on a compact metric space X is a sub-linear and bounded operator on the space of continuous functions on X. A strong submeasure is positive if it is non-decreas…
Strong submeasures and several applications
Tuyen Trung Truong
A strong submeasure on a compact metric space X is a sub-linear and bounded operator on the space of continuous functions on X. A strong submeasure is positive if it is non-decreas…
Étale dynamical systems and topological entropy
Tuyen Trung Truong
In this paper, we consider two questions about topological entropy of dynamical systems. We propose to resolve these questions by the same approach of using étale analogs of topolo…
Growth of the number of periodic points for meromorphic maps
Tien-Cuong Dinh, Viet-Anh Nguyen, Tuyen Trung Truong
We show that any dominant meromorphic self-map f of a compact Kaehler manifold X is an Artin-Mazur map. More precisely, if P_n(f) is the number of its isolated periodic points of p…
Some dynamical properties of pseudo-automorphisms in dimension 3
Tuyen Trung Truong
Let be a compact Kähler manifold of dimension 3 and let be a pseudo-automorphism. Under the mild condition that , we prove the existence of…
Equidistribution for meromorphic maps with dominant topological degree
Tien-Cuong Dinh, Viet-Anh Nguyen, Tuyen Trung Truong
Let f be a meromorphic self-map on a compact Kaehler manifold whose topological degree is strictly larger than the other dynamical degrees. We show that repelling periodic points a…
On automorphisms of blowups of projective manifolds
Tuyen Trung Truong
In this paper we mainly study the following question: For what projective manifold of dimension that any has zero topological entropy? Using some non-van…
The simplicity of the first spectral radius of a meromorphic map
Tuyen Trung Truong
Let be a compact Kähler manifold and let be a dominant rational map which is 1-stable. Let and be the first and second dynamical degrees of .…
On automorphisms of blowups of
Tuyen Trung Truong
Let be a finite composition of blowups along smooth centers. We show that for "almost all" of such , if then its first and second dyn…
Quasi-potentials and regularization of currents, and applications
Tuyen Trung Truong
Let be a compact Kähler manifold. We show that the weak regularization of Dinh and Sibony for the diagonal (see Section 2 for more detail) is compatible with wedge…
On the dynamical degrees of meromorphic maps preserving a fibration
Tien-Cuong Dinh, Viet-Anh Nguyen, Tuyen Trung Truong
Let f be a dominant meromorphic self-map on a compact Kaehler manifold X which preserves a fibration given by a meromorphic map from X to a compact Kaehler manifold Y. We compute t…
Pull-back of currents by meromorphic maps
Tuyen Trung Truong
Let and be compact Kähler manifolds, and let be a dominant meromorphic map. Base upon a regularization theorem of Dinh and Sibony for DSH currents, we de…
Degree complexity of birational maps related to matrix inversion: Symmetric case
Tuyen Trung Truong
For , we let denote the projectivization of the set of symmetric matrices with coefficients in . We let denot…
Degree Complexity of Matrix Inversion
Eric Bedford, Tuyen Trung Truong
For a q by q matrix x=(x_{i,j}) we let J(x)=(x_{i,j}^{-1}) be the Hadamard inverse, which takes the reciprocal of the elements of x . We let I(x)=(x_{i,j})^{-1} denote the matrix i…
Degree complexity of a family of birational maps: II. Exceptional cases
Tuyen Trung Truong
We compute the degree complexity of the family of birational maps considered in \cite{bedford-kim-tuyen-abarenkova-maillard} for all exceptional cases. Some interesting properties…
Degree Complexity of a Family of Birational Maps
Eric Bedford, Kyounghee Kim, Truong Trung Tuyen +2
We compute the degree complexity of a family of birational mappings of the plane with high order singularities.