Zobrazeno 1 - 10
of 150
pro vyhledávání: '"Nogueira, Arnaldo"'
We show that the complexity of the billiard in a typical polygon grows cubically and the number of saddle connections grows quadratically along certain subsequences. It is known that the set of points whose first n-bounces hits the same sequence of s
Externí odkaz:
http://arxiv.org/abs/2312.04133
We study maps of the unit interval whose graph is made up of two increasing segments and which are injective in an extended sense. Such maps $f_{\p}$ are parametrized by a quintuple $\p$ of real numbers satisfying inequations. Viewing $f_{\p}$ as a c
Externí odkaz:
http://arxiv.org/abs/2212.10944
Autor:
Nogueira, Arnaldo, Troubetzkoy, Serge
We show the chess billiard map, which was introduced in [HM] in order to study a generalization of the $n$-Queens problem in chess, is a circle homeomorphism. We give a survey of some of the known results on circle homeomorphisms, and apply them to t
Externí odkaz:
http://arxiv.org/abs/2007.14773
Autor:
Gaivão, José Pedro, Nogueira, Arnaldo
Let $I_1=[a_0,a_1),\ldots,I_{k}= [a_{k-1},a_k)$ be a partition of the interval $I=[0,1)$ into $k$ subintervals. Let $f:I\to I$ be a map such that each restriction $f|_{I_i}$ is an increasing Lipschitz contraction. We prove that any $f$ admits at most
Externí odkaz:
http://arxiv.org/abs/2007.08014
We prove that these Cantor sets are made up of transcendental numbers, apart from their endpoints $0$ and $1$, under some arithmetical assumptions on the data. To that purpose, we establish a criterion of linear independence over the field of algebra
Externí odkaz:
http://arxiv.org/abs/2001.00380
Autor:
Laurent, Michel, Nogueira, Arnaldo
Let $f : [0,1)\rightarrow [0,1)$ be a $2$-interval piecewise affine increasing map which is injective but not surjective. Such a map $f$ has a rotation number and can be parametrized by three real numbers. We make fully explicit the dynamics of $f$ t
Externí odkaz:
http://arxiv.org/abs/1907.08655
Autor:
Dani, S. G., Nogueira, Arnaldo
Let $\Gamma$ be the multiplicative semigroup of all $n\times n$ matrices with integral entries and positive determinant. Let $1\leq p \leq n-1$ and $V=\R^n\oplus \cdots \oplus \R^n$ ($p$ copies). We consider the componentwise action of $\Gamma$ on $V
Externí odkaz:
http://arxiv.org/abs/1902.09219
Autor:
Laurent, Michel, Nogueira, Arnaldo
Let $0<\lambda<1$. We consider the one-parameter family of circle $\lambda$-affine contractions $f_\delta:x \in [0,1) \mapsto \lambda x + \delta \; {\rm mod}\,1 $, where $0 \le \delta <1$. Let $\rho$ be the rotation number of the map $f_\delta$. We w
Externí odkaz:
http://arxiv.org/abs/1704.05130
Akademický článek
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Let $-1<\lambda<1$ and $f:[0,1)\to\mathbb{R}$ be a piecewise $\lambda$-affine map, that is, there exist points $0=c_0
Externí odkaz:
http://arxiv.org/abs/1605.03470