Related papers: On the entropy for group actions on the circle

Aiming at a better understanding of finite groups as finite dynamical systems, we show that by a version of Fitting's Lemma for groups, each state space of an endomorphism of a finite group is a graph tensor product of a finite directed…

We show that the set of all commuting probabilities in finite rings is a subset of the set of all commuting probabilities in finite nilpotent groups of class $\le2$. We believe that these two sets are equal; we prove they are equal, when…

We study loops of symplectic diffeomorphisms of closed symplectic manifolds. Our main result, which is valid for a large class of symplectic manifolds, shows that the flux of a symplectic loop vanishes whenever its orbits are contractible.…

We show that the automorphism group of every zero entropy infinite shift admits a "drift" homomorphism to $(\mathbb{R},+)$ that maps the shift map to 1. This homomorphism arises as the expectation, under an invariant measure, of a cocycle…

In this paper, we prove that for any $C^1$ surface diffeomorphism $f$ with positive topological entropy, there exists a diffeomorphism $g$ arbitrarily close (in the $C^1$ topology) to $f$ exhibiting a horseshoe $\Lambda$, such that the…

In a previous paper the author constructed biinvariant measures (possibly having values in a line bundle) for a loop group LK (with compact simply connected K) acting on the formal completion of its complexification LG. One motivation for…

For quantum critical spin chains without disorder, it is known that the entanglement of a segment of N>>1 spins with the remainder is logarithmic in N with a prefactor fixed by the central charge of the associated conformal field theory. We…

We define boundedness properties on the contractible fixed points set of the time-one map of an identity isotopy on a closed oriented surface with genus $g\geq1$. In symplectic geometry, a classical object is the notion of action function,…

Sofic entropy theory is a generalization of the classical Kolmogorov-Sinai entropy theory to actions of large class of non-amenable groups called sofic groups. This is a short introduction with a guide to the literature.

We show that under local detailed balance the expected entropy production rate is always bounded in terms of the dynamical activity. The activity refers to the time-symmetric contribution in the action functional for path-space…

We study the dynamics of iteration function systems generated by a pair of circle diffeomorphisms close to rotations in the $C^{1+\mathrm{bv}}$-topology. We characterize the obstruction to minimality and describe the limit set. In…

For any C1 diffeomorphism with dominated splitting we consider a nonempty set of invariant measures which describes the asymptotic statistics of Lebesgue-almost all orbits. They are the limits of convergent subsequences of averages of the…

We prove the topological entropy remains constant inside the class of partially hyperbolic diffeomorphisms of $\mathbb{T}^d$ with simple central bundle (that is, when it decomposes into one dimensional sub-bundles with controlled geometry)…

We show that on groups generated by bounded activity automata, every symmetric, finitely supported probability measure has the Liouville property. More generally we show this for every group of automorphisms of bounded type of a rooted…

We study the flux homomorphism for closed forms of arbitrary degree, with special emphasis on volume forms and on symplectic forms. The volume flux group is an invariant of the underlying manifold, whose non-vanishing implies that the…

We propose an entropic geometrical model of crowd behavior dynamics (with dissipative crowd kinematics), using Feynman action--amplitude formalism that operates on three synergetic levels: macro, meso and micro. The intent is to explain the…

We show that the entropy of a hyperbolic group acting on its ideal boundary is closely related to the exponential rate of its growth.

In this paper, we discuss asymptotic behavior of the capacity of the range of symmetric simple random walks on finitely generated groups. We show the corresponding strong law of large numbers and central limit theorem.

We prove an entropy formula for certain expansive actions of a countable discrete residually finite group $\Gamma $ by automorphisms of compact abelian groups in terms of Fuglede-Kadison determinants. This extends an earlier result proved…

We compute the polynomial entropy of the induced maps on hyperspace for a homeomorphism $f$ of an interval or a circle with finitely many non-wandering points.