Work

Non-unique equilibrium measures and freezing phase transitions for matrix cocycles for negative t

Year: 2026

Type: article

Abstract: We consider the one-step matrix cocycle generated by a particular pair of non-negative parabolic matrices and study the equilibrium measures for t log ⁡ ‖ A ‖ as t runs over the reals. We show that there is a freezing first order phase transition at t = − 2 so that for t ⩽ − 2 the equilibrium measure is non-unique and supported on the two fixed points, while for t > − 2 , the equilibrium measure is unique, non-atomic and fully supported. The phase transition closely resembles the classical Hofbauer example. In particular, our example shows that there may be non-unique equilibrium measures for negative t even if the cocycle is strongly irreducible and proximal.

Source: Nonlinearity

DOI: 10.1088/1361-6544/ae341f

Authors: Reza Mohammadpour, Anthony Quas

Institutions: Uppsala University, University of Victoria

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

Funders: Vetenskapsrådet, Natural Sciences and Engineering Research Council of Canada