Related papers: Common Limits of Fibonacci Circle Maps

We consider a generic Fibonacci topological wave function on a square lattice, and the norm of this wave function can be mapped into the partition function of two-coupled $\phi ^{2}$-state Potts models with $\phi =(\sqrt{5}+1)/2$ as the…

Consider Ginibre's ensemble of $N \times N$ non-Hermitian random matrices in which all entries are independent complex Gaussians of mean zero and variance $\frac{1}{N}$. As $N \uparrow \infty$ the normalized counting measure of the…

We consider the map $T_{\alpha,\beta}(x):= \beta x + \alpha \mod 1$, which admits a unique probability measure of maximal entropy $\mu_{\alpha,\beta}$. For $x \in [0,1]$, we show that the orbit of $x$ is $\mu_{\alpha,\beta}$-normal for…

We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together…

We consider convex maps f:R^n -> R^n that are monotone (i.e., that preserve the product ordering of R^n), and nonexpansive for the sup-norm. This includes convex monotone maps that are additively homogeneous (i.e., that commute with the…

In the last years the attention towards topological dynamical properties of highly discontinuous maps has increased significantly. In [D.Corona, A. Della Corte. The critical exponent functions. Comptes Rendus Math\'ematique, 360(G4),…

For maps of one complex variable, $f$, given as the sum of a degree $n$ power map and a degree $d$ polynomial, we provide necessary and sufficient conditions that the geometric limit as $n$ approaches infinity of the set of points that…

We consider the mean curvature evolution of rotationally symmetric surfaces. Using numerical methods, we detect critical behavior at the threshold of singularity formation resembling the one of gravitational collapse. In particular, the…

We consider piecewise $C^2$ non-flat maps of the interval and show that, for Lebesgue almost every point, its omega-limit set is either a periodic orbit, a cycle of intervals or the closure of the orbits of a subset of the critical points.…

In the setting of Carnot groups, we are concerned with the rectifiability problem for subsets that have finite sub-Riemannian perimeter. We introduce a new notion of rectifiability that is, possibly, weaker than the one introduced by…

This is the first in a series of three papers where we study the integral manifolds of the charged three-body problem. The integral manifolds are the fibers of the map of integrals. Their topological type may change at critical values of…

We prove the upper-semi-continuity of the Morse index plus nullity of critical points to general conformally invariant Lagrangians in dimension 2 under weak convergence. Precisely we establish that the sum of the Morse indices and the…

We give an upper bound for the topological entropy of maps on inverse limit spaces in terms of their set-valued components. In a special case of a diagonal map on the inverse limit space $\underleftarrow{\lim}(I,f)$, where every diagonal…

Let $(M^4,g)$ be a closed Riemannian manifold of dimension four. We investigate the properties of metrics which are critical points of the eigenvalues of the Paneitz operator when considered as functionals on the space of Riemannian metrics…

We show how measuring real space properties such as the charge density in a quasiperiodic system can be used to gain insight into their topological properties. In particular, for the Fibonacci chain, we show that the total onsite charge…

We study the localization of sets with constant nonlocal mean curvature and prescribed small volume in a bounded open set with smooth boundary, proving that they are {\em sufficiently close} to critical points of a suitable non-local…

Motivated by the appearance of embeddings in the theory of chip firing and the critical group of a graph, we introduce a version of the critical group (or sandpile group) for combinatorial maps, that is, for graphs embedded in orientable…

Criteria for piecewise linear circle homeomorphisms to be conjugate to a rigid rotation, $x\to x+\omega~({\rm mod}~1)$, with rational rotation number $\omega$ are given. The consequences of the existence of such maps in families of maps is…

Quasiconformal maps in the complex plane are homeomorphisms that satisfy certain geometric distortion inequalities; infinitesimally, they map circles to ellipses with bounded eccentricity. The local distortion properties of these maps give…

We prove results exploring the relationship between the fundamental group and the second Betti number of minimal symplectic fillings of lens spaces. These results unify and generalize several disparate facts appearing in the literature. The…