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Related papers: Rigidity of Furstenberg entropy under ucp maps

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Let $G$ be a locally compact second countable group equipped with an admissible non-degenerate Borel probability measure $\mu$. We generalize the notion of $\mu$-stationary systems to $\mu$-stationary $G$-factor maps $\pi: (X,\nu)\to…

Dynamical Systems · Mathematics 2024-05-28 Tattwamasi Amrutam , Martin Klötzer , Hanna Oppelmayer

We define the notion of self-tracial stability for tracial von Neumann algebras and show that a tracial von Neumann algebra satisfying the Connes Embedding Problem is self-tracially stable if and only if it is amenable. We then generalize a…

Operator Algebras · Mathematics 2020-05-18 Scott Atkinson , Srivatsav Kunnawalkam Elayavalli

Given a closed, orientable surface of constant negative curvature and genus $g \ge 2$, we study the topological entropy and measure-theoretic entropy (with respect to a smooth invariant measure) of generalized Bowen--Series boundary maps.…

Dynamical Systems · Mathematics 2022-10-10 Adam Abrams , Svetlana Katok , Ilie Ugarcovici

We establish several classification results for compact extensions of tracial $W^*$-dynamical systems and for relatively independent joinings thereof for actions of arbitrary discrete groups. We use these results to answer a question of…

Operator Algebras · Mathematics 2025-09-29 Asgar Jamneshan , Pieter Spaas

We prove two rigidity theorems for maps between Riemannian manifolds. First, we prove that a Lipschitz map $f:M\to N$ between two oriented Riemannian manifolds, whose differential is almost everywhere an orientation-preserving isometry, is…

Differential Geometry · Mathematics 2019-01-23 Raz Kupferman , Cy Maor , Asaf Shachar

We study stationary actions of locally compact measured groups through the structure and regularity of their Radon-Nikodym cocycles. We start with two dynamical consequences of stationarity. Extending a theorem of Furstenberg-Glasner from…

Dynamical Systems · Mathematics 2026-04-14 Nachi Avraham-Re'em , Michael Björklund

The stability of persistence diagrams is among the most important results in applied and computational topology. Most results in the literature phrase stability in terms of the bottleneck distance between diagrams and the $\infty$-norm of…

Algebraic Topology · Mathematics 2025-07-11 Primoz Skraba , Katharine Turner

We prove the first rigidity and classification theorems for crossed product von Neumann algebras given by actions of non-discrete, locally compact groups. We prove that for arbitrary free probability measure preserving actions of connected…

Operator Algebras · Mathematics 2018-07-20 Arnaud Brothier , Tobe Deprez , Stefaan Vaes

We determine Furstenberg entropy spectra of ergodic stationary actions of $SL(d,\mathbb{R})$ and its lattices. The constraints on entropy spectra are derived from a refinement of the Nevo-Zimmer projective factor theorem. The realisation…

Dynamical Systems · Mathematics 2023-07-06 Jérémie Brieussel , Tianyi Zheng

We investigate the multiplier rigidity problem for polynomial automorphisms of $\mathbf{C}^2$. A first result states that a complex H\'enon map of given degree is determined up to finitely many choices by its multiplier spectrum, or more…

Dynamical Systems · Mathematics 2026-03-11 Serge Cantat , Romain Dujardin

A general method for proving continuity of the von Neumann entropy on subsets of positive trace-class operators is considered. This makes it possible to re-derive the known conditions for continuity of the entropy in more general forms and…

Mathematical Physics · Physics 2015-05-13 M. E. Shirokov

Density of stable maps is the common thread of this paper. We review Whitney's contribution to singularities of differentiable mappings and Thom-Mather theories on $C^{\infty}$ and $C^{0}$-stability. Infinitesimal and algebraic methods are…

Dynamical Systems · Mathematics 2022-01-12 Maria Aparecida Soares Ruas

We investigate the situation when a normal positive linear unital map on a semifinite von Neumann algebra leaving the trace invariant does not change fixed quantum Renyi's entropy of the density of a normal state. It is also shown that such…

Operator Algebras · Mathematics 2023-02-07 Andrzej Łuczak , Hanna Podsędkowska , Rafał Wieczorek

We show that for every "locally finite" unit-preserving completely positive map P acting on a C*-algebra, there is a corresponding *-automorphism \alpha of another unital C*-algebra such that the two sequences P, P^2,P^3,... and \alpha,…

Operator Algebras · Mathematics 2007-05-23 William Arveson

We show that for families of measures on Euclidean space which satisfy an ergodic-theoretic form of "self-similarity" under the operation of re-scaling, the dimension of linear images of the measure behaves in a semi-continuous way. We…

Dynamical Systems · Mathematics 2014-09-23 Michael Hochman , Pablo Shmerkin

It is known that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of ${\fR}^2$. A renormalization approach has been used in \cite{EKW1} and \cite{EKW2} in a computer-assisted…

Dynamical Systems · Mathematics 2010-02-07 Denis Gaidashev , Tomas Johnson

A mapping $f: {\mathcal M} \to {\mathcal N}$ between Hilbert $C^*$-modules approximately preserves the inner product if \[\|< f(x), f(y)> - < x, y> \| \leq \phi(x, y),\] for an appropriate control function $\phi(x,y)$ and all $x, y \in…

Operator Algebras · Mathematics 2008-04-30 Jacek Chmielinski , Mohammad Sal Moslehian

We study the problem of extending an order-preserving real-valued Lipschitz map defined on a subset of a partially ordered metric space without increasing its Lipschitz constant and preserving its monotonicity. We show that a certain type…

Functional Analysis · Mathematics 2023-05-02 Efe A. Ok

We present a bouquet of continuity bounds for quantum entropies, falling broadly into two classes: First, a tight analysis of the Alicki-Fannes continuity bounds for the conditional von Neumann entropy, reaching almost the best possible…

Quantum Physics · Physics 2016-09-06 Andreas Winter

We give various characterizations for a positive unital Tr-preserving map on a matrix algebra to preserve the von Neumann entropy of a state. Among others, it is given by that the map behaves as a *-automorphism. This is also equivalent to…

Operator Algebras · Mathematics 2014-09-15 Marie Choda
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