Related papers: Still Baking

Let X and Y be compact, simply connected and locally connected subsets of R^2, and let f : X -> Y be a homeomorphism isotopic to the identity on X. Generalizing Brouwer's plane translation theorem for self-maps of the plane, we prove that f…

Let $G=\mathrm{SL}(2,\mathbb{Z})\ltimes\mathbb{Z}^2$ and $H=\mathrm{SL}(2,\mathbb{Z})$. We prove that the action $G\curvearrowright\mathbb{R}^2$ is uniformly non-amenable and that the quasi-regular representation of $G$ on $\ell^2(G/H)$ has…

Michael Handel proved in [7] the existence of a fixed point for an orientation preserving homeomorphism of the open unit disk that can be extended to the closed disk, provided that it has points whose orbits form an oriented cycle of links…

We propose a generalization of the model of classical baker map on the torus, in which the images of two parts of the phase space do overlap. This transformation is irreversible and cannot be quantized by means of a unitary Floquet…

Assuming Lang's conjectured lower bound on the heights of non-torsion points on an elliptic curve, we show that there exists an absolute constant C such that for any elliptic curve E/Q and non-torsion point P in E(Q), there is at most one…

We use $KKM$ theorem to prove the existence of a new fixed point theorem for non-expansive mapping:Let M be a bounded closed convex subset of Hilbert space H, and $A:M\rightarrow M$ be a non-expansive mapping, then exists a fixed point of A…

If $f:[a,b]\to \mathbb{R}$, with $a<b$, is continuous and such that $a$ and $b$ are mapped in opposite directions by $f$, then $f$ has a fixed point in $I$. Suppose that $f:\mathbb{C}\to\mathbb{C}$ is map and $X$ is a continuum. We extend…

For chaotic classical systems, the distribution of return times to a small region of phase space is universal. We propose a simple tool to investigate multiple returns in quantum systems. Numerical evidence for the baker map and kicked top…

For linear operators $L, T$ and nonlinear maps $P$, we describe classes of simple maps $F = I - P T$, $F = L - P$ between Banach and Hilbert spaces, for which no point has more than two preimages. The classes encompass known examples…

Our main goal in this paper is to prove existence (and uniqueness) of the quantum propagator for time dependent quantum Hamiltonians $\hat H(t)$ when this Hamiltonian is perturbed with a quadratic white noise $\dot{\beta}\hat K$. $\beta$ is…

The aim of this paper is to give another proof to a result on the image of a homogeneous quadratic map which is positive with respect to a homogeneous cone, given by Graczyk and Ishi in 2014. The new proof depends on a purely algebraic…

For piecewise $C^1$ interval maps possibly containing critical points and discontinuities with negative Schwarzian derivative, under two summability conditions on the growth of the derivative and recurrence along critical orbits, we prove…

We consider some perturbations of a family of pairwise commuting linear quantum Hamiltonians on the torus with possibly dense pure point spectra. We prove that the Rayleigh-Schr{\"o}dinger perturbation series converge near each unperturbed…

We study the pointwise perturbations of countable Markov maps with infinitely many inverse branches and establish the following continuity theorem: Let $T_k$ and $T$ be expanding countable Markov maps such that the inverse branches of $T_k$…

We exhibit some arguments in favour of an H-theorem for a generalization of the Boltzmann equation including non-conservative interactions and a linear Fokker-Planck-like thermostatting term. Such a non-linear equation describing the…

Let $G$ denote a complex semisimple linear algebraic group, $P$ a parabolic subgroup of $G$ and $\mathcal{P}=G/P$. We identify the quantum multiplication by divisors in $T^*\mathcal{P}$ in terms of stable basis, which is introduced by…

We prove that for certain partially hyperbolic skew-products, non-uniform hyperbolicity along the leaves implies existence of a finite number of ergodic absolutely continuous invariant probability measures which describe the asymptotics of…

This paper is devoted to study the topological invariance of several non-uniform hyperbolicity conditions of one-dimensional maps. In contrast with the case of maps with only one critical point, it is known that for maps with several…

In this paper, we give a new proof of the classical KAM theorem on the persistence of an invariant quasi-periodic torus, whose frequency vector satisfies the Bruno-R\"ussmann condition, in real-analytic non-degenerate Hamiltonian systems…

Let $E/F$ be a quadratic extension of finite fields. By a result of Gow, an irreducible representation $\pi$ of $G = {\rm GL}_n(E)$ has at most one non-zero $H$-invariant vector, up to multiplication by scalars, when $H$ is ${\rm GL}_n(F)$…