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The Real Fatou Conjecture. (Am-144)
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Jacek Graczyk, Grzegorz Swiatek
In 1920, Pierre Fatou expressed the conjecture that - except for special cases - all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. This conjecture remains the main open problem in the dynamics of iterated maps. For the logistic family x- ax(1-x), it can be interpreted to mean that for a dense set ...
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Combinatorics of Train Tracks
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R C Penner, John L Harer
Measured geodesic laminations are a natural generalization of simple closed curves in surfaces, and they play a decisive role in various developments in two-and three-dimensional topology, geometry and dynamical systems. This book presents a self-contained treatment of the combinatorial structure of the space of measured geodesic laminations in a ...
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The Geometry of Geodesics
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Herbert Busemann
A comprehensive approach to qualitative problems in intrinsic differential geometry, this text opens with an explanation of the basic concepts and proceeds to discussions of Desarguesian spaces, perpendiculars and parallels, and covering spaces. Concluding chapters examine the influence of the sign of the curvature on geodesics and homogenous ...
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Plane Networks and Their Applications
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Kai Borre
This text introduces the concepts and applications behind plane networks. The book presents features on: fundamental material includin linear algebra and differential equations; an examination of tools for analyzing discrete networks; transition from the discrete to the continuous case is described via finite elements; Green's functions; problems ...
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The variational theory of geodesics
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M M Postnikov
Compact, self-contained text by noted theorist presents the most fundamental aspects of modern differential geometry as well as the basic tools required for the study of Morse theory. Advanced treatment; analytical rather than topological aspects of Morse theory emphasized. Discusses smooth manifolds, spaces of affine connection, Riemannian spaces ...
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Manifolds All of Whose Geodesics Are Closed
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A L Besse
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Sub-Riemannian Geometry: General Theory and Examples
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Ovidiu Calin, Der-Chen Chang
Sub-Riemannian manifolds are manifolds with the Heisenberg principle built in. This comprehensive text and reference begins by introducing the theory of sub-Riemannian manifolds using a variational approach in which all properties are obtained from minimum principles, a robust method that is novel in this context. The authors then present examples ...
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Variational Methods in Lorentzian Geometry
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Antonio Maisello, Antonio Masiello
The aim of this work is to apply variational methods and critical point theory on infinite dimensional manifolds, to some problems in Lorentzian Geometry which have a variational nature, such as existence and multiplicity results on geodesics and Relations between such geodesics and the topology of the manifold (in the spirit of Morse Theory). In ...
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Lectures on Closed Geodesics
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W Klingenberg
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Integrable Hamiltonian Systems: Geometry, Topology, Classification
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A T Fomenko, A V Bolsinov, Bolsinov Bolsinov
Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and the general theory underlying their qualitative properties, singularites, and topological invariants.The authors, both ...
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Spaces with Distinguished Geodesics
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Bhalchandra, B. B. Phadke, Herbert Busemann
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Shortest Paths for Sub-Riemannian Metrics on Rank-Two Distributions
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Wensheng Liu
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Tour of Subriemannian Geometries, Their Geodesics, and Applications
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R Montgomery
Subriemannian geometries, also known as Carnot-Caratheodory geometries, can be viewed as limits of Riemannian geometries. They also arise in physical phenomenon involving "geometric phases" or holonomy. Very roughly speaking, a subriemannian geometry consists of a manifold endowed with a distribution (meaning a $k$-plane field, or subbundle of the ...
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Selberg Trace Formulae and Equidistribution Theorems for Closed Geodesics and Laplace Eigenfunctions: Finite Area Surfaces
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Steven Zelditch
This work is concerned with a pair of dual asymptotics problems on a finite-area hyperbolic surface. The first problem is to determine the distribution of closed geodesics in the unit tangent bundle. The author's results give a quantitative form to Bowen's equidistribution theory: they refine Bowen's theorem much as the prime geodesic theorem on ...
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Two Classes of Riemannian Manifolds Whose Geodesic Flows Are Integrable
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Kazuyoshi Kiyohara
In this work, two classes of manifolds whose geodesic flows are integrable are defined, and their global structures are investigated. They are called Liouville manifolds and Kahler-Liouville manifolds respectively. In each case, the author finds several invariants with which they are partly classified. The classification indicates, in particular, ...
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Behavior of Distant Maximal Geodesics in Finitely Connected Complete 2-Dimensional Riemannian Manifo
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Takashi Shioya
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Geodesics and Ends in Certain Surfaces Without Conjugate Points
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Patrick B. Eberlein
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Lectures on geodesics in Riemannian geometry
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Marcel Berger
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Über die Existenz unendlich vieler geschlossener Geodätischer
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Wilhelm Klingenberg
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