The Experts below are selected from a list of 4515 Experts worldwide ranked by ideXlab platform
Maurice Margenstern - One of the best experts on this subject based on the ideXlab platform.
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the tilings f p, qg of the Hyperbolic Plane when q is odd
2020Co-Authors: Maurice MargensternAbstract:In this paper, we remind previous results about the tilings {p, q} of the Hyperbolic Plane. We introduce two new ways to split the Hyperbolic Plane in order to algorithmically construct the tilings {p, q} when q is odd.
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THE FINITE TILING PROBLEM IS UNDECIDABLE IN THE Hyperbolic Plane
International Journal of Foundations of Computer Science, 2020Co-Authors: Maurice MargensternAbstract:In this paper, we consider the finite tiling problem which was proved undecidable in the Euclidean Plane by Jarkko Kari, see [5]. Here, we prove that the same problem for the Hyperbolic Plane is also undecidable.
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Infinigons of the Hyperbolic Plane and grossone
Applied Mathematics and Computation, 2016Co-Authors: Maurice MargensternAbstract:In this paper, we study the contribution of the theory of grossone to the study of infinigons in the Hyperbolic Plane. We can see that the theory of grossone can help us to obtain a much more precise classification for these objects than in the traditional setting.
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About embedded quarters and points at infinity in the Hyperbolic Plane
arXiv: Computational Geometry, 2015Co-Authors: Maurice MargensternAbstract:In this paper, we prove two results. First, there is a family of sequences of embedded quarters of the Hyperbolic Plane such that any sequence converges to a limit which is an end of the Hyperbolic Plane. Second, there is no algorithm which would allow us to check whether two given ends are equal or not.
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Infinigons of the Hyperbolic Plane and grossone
arXiv: Discrete Mathematics, 2015Co-Authors: Maurice MargensternAbstract:In this paper, we study the contribution of the theory of grossone to the study of infinigons in the Hyperbolic Plane. We can see that the theory of grossone can help us to obtain much more classification for these objects than in the traditional setting.
C Goodmanstrauss - One of the best experts on this subject based on the ideXlab platform.
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a hierarchical strongly aperiodic set of tiles in the Hyperbolic Plane
Theoretical Computer Science, 2010Co-Authors: C GoodmanstraussAbstract:We give a new construction of strongly aperiodic set of tiles in H^2, exhibiting a kind of hierarchical structure, simplifying the central framework of Margenstern's proof that the Domino Problem is undecidable in the Hyperbolic Plane (Margenstern (2008) [16]).
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a strongly aperiodic set of tiles in the Hyperbolic Plane
Inventiones Mathematicae, 2005Co-Authors: C GoodmanstraussAbstract:We construct the first known example of a strongly aperiodic set of tiles in the Hyperbolic Plane. Such a set of tiles does admit a tiling, but admits no tiling with an infinite cyclic symmetry. This can also be regarded as a “regular production system” [5] that does admit bi-infinite orbits, but admits no periodic orbits.
Yuri L. Sachkov - One of the best experts on this subject based on the ideXlab platform.
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Integrability by quadratures in optimal control of a unicycle on Hyperbolic Plane
2015 American Control Conference (ACC), 2015Co-Authors: Yasir Awais Butt, Aamer Iqbal Bhatti, Yuri L. SachkovAbstract:We consider the problem of integrability by quadratures of normal Hamiltonian system in sub-Riemannian problem on the groups of motions of Hyperbolic Plane or pseudo Euclidean Plane which form the Lie group SH(2). The first step towards proof of integrability is to calculate the local representation of the Lie group SH(2) in canonical coordinates of second kind. Wei-Norman transformation is applied to obtain this local representation. The Wei-Norman representation shows that the left invariant control system defined on the Lie group SH(2) is equivalent to the motion of a unicycle on Hyperbolic Plane. Three integrals of motion satisfying the Liouville's integrability conditions are then calculated to prove that the normal Hamiltonian system is integrable by quadratures.
Itai Benjamini - One of the best experts on this subject based on the ideXlab platform.
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Continuous Versus Discrete Spins in the Hyperbolic Plane
Journal of Statistical Physics, 2017Co-Authors: Itai Benjamini, Gady KozmaAbstract:We study the O(n) model on graphs quasi-isometric to the Hyperbolic Plane, with free boundary conditions. We observe that the pair correlation decays exponentially with distance, for all temperatures, if and only if \(n>1.\)
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The Hyperbolic Plane and Hyperbolic Graphs
Lecture Notes in Mathematics, 2013Co-Authors: Itai BenjaminiAbstract:The aim of this section is to give a very short introduction to planar Hyperbolic geometry. Some good references for parts of this section are [CFKP97] and [ABC+91]. We first discuss the Hyperbolic Plane. Nets in the Hyperbolic Plane are concrete examples of the more general Hyperbolic graphs. Hyperbolicity is reflected in the behaviour of random walks [Anc88] and percolation as we will see in Chap. 7.
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percolation in the Hyperbolic Plane
Journal of the American Mathematical Society, 2000Co-Authors: Itai Benjamini, Oded SchrammAbstract:The purpose of this paper is to study percolation in the Hyperbolic Plane and in transitive planar graphs that are quasi-isometric to the Hyperbolic Plane.
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percolation in the Hyperbolic Plane
arXiv: Probability, 1999Co-Authors: Itai Benjamini, Oded SchrammAbstract:This is a study of percolation in the Hyperbolic Plane and on regular tilings in the Hyperbolic Plane. The processes discussed include Bernoulli site and bond percolation on planar Hyperbolic graphs, invariant dependent percolations on such graphs, and Poisson-Voronoi-Bernoulli percolation. We prove the existence of three distinct nonempty phases for the Bernoulli processes. In the first phase, $p\in(0, p_c]$, there are no unbounded clusters, but there is a unique infinite cluster for the dual process. In the second phase, $p\in(p_c,p_u)$, there are infinitely many unbounded clusters for the process and for the dual process. In the third phase, $p\in [p_u,1)$, there is a unique unbounded cluster, and all the clusters of the dual process are bounded. We also study the dependence of $p_c$ in the Poisson-Voronoi-Bernoulli percolation process on the intensity of the underlying Poisson process.
Oded Schramm - One of the best experts on this subject based on the ideXlab platform.
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percolation in the Hyperbolic Plane
Journal of the American Mathematical Society, 2000Co-Authors: Itai Benjamini, Oded SchrammAbstract:The purpose of this paper is to study percolation in the Hyperbolic Plane and in transitive planar graphs that are quasi-isometric to the Hyperbolic Plane.
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percolation in the Hyperbolic Plane
arXiv: Probability, 1999Co-Authors: Itai Benjamini, Oded SchrammAbstract:This is a study of percolation in the Hyperbolic Plane and on regular tilings in the Hyperbolic Plane. The processes discussed include Bernoulli site and bond percolation on planar Hyperbolic graphs, invariant dependent percolations on such graphs, and Poisson-Voronoi-Bernoulli percolation. We prove the existence of three distinct nonempty phases for the Bernoulli processes. In the first phase, $p\in(0, p_c]$, there are no unbounded clusters, but there is a unique infinite cluster for the dual process. In the second phase, $p\in(p_c,p_u)$, there are infinitely many unbounded clusters for the process and for the dual process. In the third phase, $p\in [p_u,1)$, there is a unique unbounded cluster, and all the clusters of the dual process are bounded. We also study the dependence of $p_c$ in the Poisson-Voronoi-Bernoulli percolation process on the intensity of the underlying Poisson process.