arXiv Open Access 2024

Dynamical Degrees, Arithmetic Degrees, and Canonical Heights: History, Conjectures, and Future Directions

Joseph H. Silverman

Lihat Sumber

Abstrak

In this note we give an overview of various quantities that are used to measure the complexity of an algebraic dynamical system f:X-->X, including the dynamical degree d(f), which gives a coarse measure of the geometric complexity of the iterates of f, the arithmetic degree a(f,P), which gives a coarse measure of the arithmetic complexity of the orbit of a an algebraic point P in X, and various versions of the canonical height h_f(P) that provide more refined measures of arithmetic complexity. Emphasis is placed on open problems and directions for further exploration.

Topik & Kata Kunci

math.NT math.DS

Penulis (1)

Joseph H. Silverman

Format Sitasi

APA MLA BibTeX

Silverman, J.H. (2024). Dynamical Degrees, Arithmetic Degrees, and Canonical Heights: History, Conjectures, and Future Directions. https://arxiv.org/abs/2408.01559

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓