Related papers: The doubling map with asymmetrical holes

There are two free coupling parameters $c_{13}$ and $c_{14}$ in the Einstein-\AE ther metric describing a non-rotating black hole. This metric is the Reissner-Nordstr\"{o}m black hole solution when $0\leq 2c_{13}<c_{14}<2$, but it is not…

It is argued that a unitarity-violating but weakly CPT invariant superscattering matrix exists for leading-order large-$N$ dilaton gravity, if and only if one includes in the Hilbert space planckian ``thunderpop" excitations which create…

We construct representations of the Heisenberg algebra by pushing the perturbation expansion to high orders. If the multiplication operators $B_{1,2}$ tend to differential operators of order $l_{2,1}$, respectively, the singularity is…

In a Randall-Sundrum theory (RS1) 3+1 dimensional black holes and higher dimensional black holes are not the natural continuations of each other. 3+1 dimensional black holes decay into a large number of 4+1 dimensional black holes at a…

In this paper we present a new proof of the following 2010 result of Dubickas, Novikas, and Siurys: Let $(a,b)\in \mathbb{Z}^2$ and let $(x_n)_{n\ge 0}$ be the sequence defined by some initial values $x_0$ and $x_1$ and the second order…

We use heterotic/type-II prepotentials to study quantum/classical black holes with half the $N=2, D=4$ supersymmetries unbroken. We show that, in the case of heterotic string compactifications, the perturbatively corrected entropy formula…

In this article, we show that in a $Q$-doubling space $(X,d,\mu),$ $Q>1,$ that supports a $Q$-Poincar\'e inequality and satisfies a chain condition, sets of $Q$-capacity zero have generalized Hausdorff $h$-measure zero for…

We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical exploration shows that chaos is abundant at low levels of…

A wide variety of intricate dynamics may be created at border-collision bifurcations of piecewise-smooth maps, where a fixed point collides with a surface at which the map is nonsmooth. For the border-collision normal form in two…

We study the statistics of Hamiltonian cycles on various families of bicolored random planar maps (with the spherical topology). These families fall into two groups corresponding to two distinct universality classes with respective central…

We study the trajectories of massive particles in spherically symmetric black holes in arbitrary dimensions, and find certain universal features based on the topological classification of the fixed points. If the system admits a center, we…

We generalize the superposition principle for time-symmetric initial data of black hole spacetimes to (anti-)de Sitter cosmologies in terms of an eigenvalue problem $\Delta_g\phi={1/8}(R_g-2\Lambda)\phi$ for a conformal scale $\phi$ applied…

Deterministic chaos is commonly associated with spectral criticality: exponential sensitivity is expected when Jacobian eigenvalues exceed unity in parts of the attractor, producing the local expansion that offsets contraction elsewhere. We…

We study random graphs, both $G(n,p)$ and $G(n,m)$, with random orientations on the edges. For three fixed distinct vertices s,a,b we study the correlation, in the combined probability space, of the events a -> s and s -> b. For G(n,p), we…

Using $N=1+1$ supersymmetric extension of the three-dimensional gravity with torsion, we show that a generic black hole has no exact supersymmetries, the extremal black hole has only one, while the zero-energy black hole has two. Combining…

We show that for every finite colouring of the natural numbers there exists $a,b >1$ such that the triple $\{a,b,a^b\}$ is monochromatic. We go on to show the partition regularity of a much richer class of patterns involving exponentiation.…

We consider a class of doubly intermittent maps with critical points, unbounded derivative and regularly varying tails. Under some mild assumptions we prove the existence of a unique mixing absolutely continuous invariant measure and give…

In the article we consider the composite conformal map which maps annulus to infinite region with symmetric hole and nearly circular hole. It is shown that such transformation is good if the distance between centers of holes are large or…

We study the occurrence of critical phenomena in four - dimensional, rotating and charged black holes, derive the critical exponents and show that they fulfill the scaling laws. Correlation functions critical exponents and Renormalization…

We prove that a class of one-dimensional maps with an arbitrary number of non-degenerate critical and singular points admits an induced Markov tower with exponential return time asymptotics. In particular the map has an absolutely…