Related papers: A Ruelle operator for holomorphic correspondences

We give a new definition of topological pressure for arbitrary (non-compact, non-invariant) Borel subsets of metric spaces. This new quantity is defined via a suitable variational principle, leading to an alternative definition of an…

We analyse the role of vertex operator algebra and 2d amplitudes from the point of view of the representation theory of infinite dimensional Lie algebras, MacMahon and Ruelle functions. A p-dimensional MacMahon function is the generating…

In this paper we study the double transpose of the $L^1(X,\mathscr{B}(X),\nu)$-extensions of the Ruelle transfer operator $\mathscr{L}_{f}$ associated to a general real continuous potential $f\in C(X)$, where $X=E^{\mathbb{N}}$, the…

We study the behavior of the pressure function for H\"{o}lder continuous potentials on mixing subshifts of finite type. The classical theory of thermodynamic formalism shows that such pressure functions are convex, analytic and have slant…

This paper is motivated by Brolin's theorem. The phenomenon we wish to demonstrate is as follows: if $F$ is a holomorphic correspondence on $\mathbb{P}^1$, then (under certain conditions) $F$ admits a measure $\mu_F$ such that, for any…

This text provides an overview of the (geometric) thermodynamic formalism for transcendental meromorphic and entire functions with particular emphasis on geometric/fractal aspects such as Bowen's Formula expressing the hyperbolic dimension…

Given a holomorphic Hilbertian bundle on a compact complex manifold, we introduce the notion of holomorphic $L^2$ torsion, which lies in the determinant line of the twisted $L^2$ Dolbeault cohomology and represents a volume element there.…

Considering evolutionary equations in the sense of Picard, we identify a certain topology for material laws rendering the solution operator continuous if considered as a mapping from the material laws into the set of bounded linear…

Understanding and predicting thermal transport in disordered materials remains a significant challenge due to the absence of periodicity and the complex nature of medium-range structural motifs. In this work, we investigate amorphous…

We discuss how one uses the thermodynamic formalism to produce metrics on higher Teichm\"uller spaces. Our higher Teichm\"uller spaces will be spaces of Anosov representations of a word-hyperbolic group into a semi-simple Lie group. We…

We study toroidal orbifold models with topologically invariant terms in the path integral formalism and give physical interpretations of the terms from an operator formalism point of view. We briefly discuss a possibility of a new class of…

We show how changes in unitarity-preserving boundary conditions allow continuous interpolation among the Hilbert spaces of quantum mechanics on topologically distinct manifolds. We present several examples, including a computation of…

It is well-known that a Rindler observer measures a non-trivial energy flux, resulting in a thermal description in an otherwise Minkowski vacuum. For systems consisting of large number of degrees of freedom, it is natural to isolate a small…

On contact manifolds we describe a notion of (contact) finite-type for linear partial differential operators satisfying a natural condition on their leading terms. A large class of linear differential operators are of finite-type in this…

We study the dynamics of the attractor of the doubling map with an asymmetrical hole by associating to each hole an element of the lexicographic world. A description of the topological entropy function is given. We show that the set of…

This paper introduces an intrinsic theory of Thermodynamic Formalism for Iterated Functions Systems with general positive continuous weights (IFSw).We study the spectral properties of the Transfer and Markov operators and one of our first…

We study thermodynamic formalism of dynamical systems with non-uniform structure. Precisely, we obtain the uniqueness of equilibrium states for a family of non-uniformly expansive flows by generalizing Climenhaga-Thompson's orbit…

Denote by $\mathbf{\mu}$ the maximal entropy measure for the shift map $\sigma$ acting on $\Omega = \{0, 1\}^\mathbb{N}$, by $L$ the associated Ruelle operator and by $K = L^{\dagger}$ the Koopman operator, both acting on…

The paper introduces Laplace-type operators for functions defined on the tangent space of a Finsler Lie algebroid, using a volume form on the prolongation of the algebroid. It also presents the construction of a horizontal Laplace operator…

We establish a state-operator correspondence for a class of non-conformal quantum field theories with continuous higher-form symmetries and a mixed anomaly. Such systems can always be realised as a relativistic superfluid. The symmetry…