Results 21 to 30 of about 74 (58)
Surfaces of Constant Curvature in the Pseudo‐Galilean Space
International Journal of Mathematics and Mathematical Sciences, Volume 2012, Issue 1, 2012., 2012 We develop the local theory of surfaces immersed in the pseudo‐Galilean space, a special type of Cayley‐Klein spaces. We define principal, Gaussian, and mean curvatures. By this, the general setting for study of surfaces of constant curvature in the pseudo‐Galilean space is provided. We describe surfaces of revolution of constant curvature.
Željka Milin Šipuš +2 more
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Equivalence of the Apollonian and Its Inner Metric
International Journal of Mathematics and Mathematical Sciences, Volume 2010, Issue 1, 2010., 2010 We show that the equivalence of the Apollonian metric and its inner metric remains unchanged by the removal of a point from the domain. For this we need to assume that the complement of the domain is not contained in a hyperplane. This improves a result of the authors wherein the same conclusion was reached under the stronger assumption that the ...
Peter Hästö +3 more
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Gromov hyperbolic equivalence of the hyperbolic and quasihyperbolic metrics in Denjoy domains [PDF]
Bulletin of the London Mathematical Society, 2010 In this article we investigate the Gromov hyperbolicity of Denjoy domains equipped with the hyperbolic or the quasihyperbolic metric. We first prove the existence of suitable families of quasigeodesics. The main result shows that a Denjoy domain is Gromov hyperbolic with respect to the hyperbolic metric if and only it is Gromov hyperbolic with respect ...
Hästö, Peter +3 more
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The Apollonian metric: limits of the comparison and bilipschitz properties
Abstract and Applied Analysis, Volume 2003, Issue 20, Page 1141-1158, 2003., 2003 The Apollonian metric is a generalization of the hyperbolic metric. It is defined in arbitrary domains in ℝn. In this paper, we derive optimal comparison results between this metric and the jG metric in a large class of domains. These results allow us to prove that Euclidean bilipschitz mappings have small Apollonian bilipschitz constants in a domain G
Peter A. Hästö
wiley +1 more source
Discrete Dynamics in Nature and Society, Volume 2, Issue 1, Page 53-72, 1998., 1998 In this paper the definition of attractor of a dissipative dynamical system is introduced. The classification of the existing types of attractors and the analysis of their characteristics are presented. The discussed problems are illustrated by the results of numerical simulations using a number of real examples that provides the possibility to ...
Vadim S. Anishchenko +1 more
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Comparative Gromov hyperbolicity results for the hyperbolic and quasihyperbolic metrics [PDF]
Complex Variables and Elliptic Equations, 2009 In this article, we investigate the Gromov hyperbolicity of Denjoy domains equipped with the hyperbolic or the quasihyperbolic metric. The focus are on comparative or decomposition results, which allow us to reduce the question of whether a given domain is Gromov hyperbolic to a series of questions concerning simpler domains.
Hästö, Peter +3 more
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Chaotic attractors of two‐dimensional invertible maps
Discrete Dynamics in Nature and Society, Volume 2, Issue 4, Page 249-256, 1998., 1998 In this paper, we investigate the characteristics of quasihyperbolic attractors and quasiattractors in Invertible dissipative maps of the plane. The criteria which allow one to diagnose the indicated types of attractors in numerical experiments are formulated.
Vadim S. Anishchenko +3 more
wiley +1 more source
Local properties of quasihyperbolic mappings in metric spaces
Annales Academiae Scientiarum Fennicae Mathematica, 2016 Summary: In this paper, we consider Väisälä's problem and obtain that a homeomorphism which is both semi-local \(M\)-QH and semi-local \(\eta\)-QS between two suitable metric spaces is an \(M_{1}\)-QH map.
Huang, Xiaojun +2 more
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Close-to-convexity of quasihyperbolic and j-metric balls
Annales Academiae Scientiarum Fennicae Mathematica, 2010 12 pages, 2 ...
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Freely quasiconformal and locally weakly quasisymmetric mappings in metric spaces
Open MathematicsIn this article, we investigate the relationship between freely quasiconformal mappings and locally weakly quasisymmetric mappings in quasiconvex and complete metric spaces.
Liu Hong-Jun +3 more
doaj +1 more source