Year: 2024
Type: article
Abstract: Two-dimensional maps with discontinuities are considered. It is shown that, in the presence of discontinuities, the essential spectrum of the transfer operator is large whenever it acts on a Banach space with norm that is stronger than $$L^\infty $$ L ∞ or $$BV$$ BV . Three classes of examples are introduced and studied, both expanding and partially expanding. In two dimensions, there is complication due to the geometry of the discontinuities, an issue not present in the one-dimensional case and which is explored in this work.
Source: Annales Henri Poincaré
Authors: Oliver Butterley, Giovanni Canestrari, Roberto Castorrini
Institutions: University of Rome Tor Vergata, Scuola Normale Superiore
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W4403344986