arXiv Open Access 2025

Ergodic and synthetic Koopman analyses of cat maps onto classical 2-tori

David Viennot

Lihat Sumber

Abstrak

We study classical continuous automorphisms of the torus (cat maps) from the viewpoint of the Koopman theory. We find analytical formulae for Koopman modes defined coherently on the whole of the torus, and their decompositions associated with the partition of the torus into ergodic components. The spectrum of the Koopman operator is studied in four cases of cat maps: cyclic, quasi-cyclic, critical (transition from quasi-cyclic to chaotic behaviour) and chaotic. The synthetic spectrum associated with the ergodic decomposition is also studied.

Topik & Kata Kunci

nlin.CD math-ph

Penulis (1)

David Viennot

Format Sitasi

APA MLA BibTeX

Viennot, D. (2025). Ergodic and synthetic Koopman analyses of cat maps onto classical 2-tori. https://arxiv.org/abs/2505.10293

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓