Topic
Transversal (combinatorics)
About: Transversal (combinatorics) is a research topic. Over the lifetime, 2459 publications have been published within this topic receiving 22984 citations. The topic is also known as: Transversal (combinatorics).
Papers published on a yearly basis
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Papers
TL;DR: In this paper, the authors consider dynamical systems resulting from the motion of a material point in domains with strictly convex boundary, that is, such that the operator of the second quadratic form is negative-definite at each point of the boundary, where the boundary is taken to be equipped with the field of inward normals.
Abstract: In this paper we consider dynamical systems resulting from the motion of a material point in domains with strictly convex boundary, that is, such that the operator of the second quadratic form is negative-definite at each point of the boundary, where the boundary is taken to be equipped with the field of inward normals. We prove that such systems are ergodic and are K-systems. The basic method of investigation is the construction of transversal foliations for such systems and the study of their properties.
1,151 citations
TL;DR: In this article, a general method is presented for the synthesis of the folded-configuration coupling matrix for Chebyshev or other filtering functions of the most general kind, including the fully canonical case, i.e., N prescribed finite position transmission zeros in an Nth-degree network.
Abstract: A general method is presented for the synthesis of the folded-configuration coupling matrix for Chebyshev or other filtering functions of the most general kind, including the fully canonical case, i.e., N prescribed finite-position transmission zeros in an Nth-degree network. The method is based on the "N+2" transversal network coupling matrix, which is able to accommodate multiple input/output couplings, as well as the direct source-load coupling needed for the fully canonical cases. Firstly, the direct method for building up the coupling matrix for the transversal network is described. A simple non-optimization process is then outlined for the conversion of the transversal matrix to the equivalent "N+2" folded-configuration coupling matrix. The folded matrix may be used directly to realize microwave bandpass filters in a variety of technologies, but some of these could require awkward-to-realize cross-couplings. This paper concludes with a description of two simple procedures for transforming the transversal and folded matrices into two novel network configurations, which enable the realization of advanced microwave bandpass filters without the need for complex inter-resonator coupling elements.
945 citations
TL;DR: In this paper, it was shown that if F has a transversal homoclinic point near it there is a Cantor-like set near it on which some iterate of F is invariant and isomorphic to the Bernoulli shift on a finite number of symbols.
610 citations
TL;DR: In this article, Margulis et al. showed that Y-conditions for a geodesic flow on manifolds of negative curvature can be verified using transversal foliations.
Abstract: CONTENTSIntroductionLecture 1. The Maupertuis-Lagrange-Jacobi principle and reduction of a dynamical system to a geodesic flow. Some general properties of smooth dynamical systemsLecture 2. Y-systemsLecture 3. Verification of the Y-conditions for a geodesic flow on manifolds of negative curvatureLecture 4. Transversal foliationsLecture 5. Measurability and absolute continuity of transversal foliations for Y-systemsConclusionAppendix. G. A. Margulis, Y-flows on three-dimensional manifoldsReferences
295 citations
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 234 |
| 2024 | 417 |
| 2023 | 315 |
| 2022 | 513 |
| 2021 | 122 |
| 2020 | 126 |