Diffeomorphism that has a hyperbolic structure on the tangent bundle
In mathematics, more particularly in the fields of dynamical systems and geometric topology, an Anosov map on a manifold M is a certain type of mapping, from M to itself, with rather clearly marked local directions of "expansion" and "contraction". Anosov systems are a special case of Axiom A systems.
Anosov diffeomorphisms were introduced by Dmitri Victorovich Anosov, who proved that their behaviour was in an appropriate sense generic (when they exist at all).[1]
^Dmitri V. Anosov, Geodesic flows on closed Riemannian manifolds with negative curvature, (1967) Proc. Steklov Inst. Mathematics. 90.
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is called an Anosov flow. A classical example of Anosovdiffeomorphism is the Arnold's cat map. Anosov proved that Anosovdiffeomorphisms are structurally...
is approximated by an Anosov system. Let M be a smooth manifold with a diffeomorphism f: M→M. Then f is an axiom A diffeomorphism if the following two...
In 2014, he died at the age of 77. AnosovdiffeomorphismAnosov map Pseudo-Anosov map "Dmitrii Viktorovich Anosov - Biography". Аносов, Дмитрий Викторович...
when the entire manifold M is hyperbolic, the map f is called an Anosovdiffeomorphism. The dynamics of f on a hyperbolic set, or hyperbolic dynamics,...
Atwood's machine Tilt A Whirl Other related topics Amplitude death Anosovdiffeomorphism Catastrophe theory Causality Chaos as topological supersymmetry...
Fractal Limit set Lyapunov exponent Orbit Periodic point Phase space Anosovdiffeomorphism Arnold tongue axiom A dynamical system Bifurcation diagram Box-counting...
structurally stable systems in arbitrary dimensions is given by Anosovdiffeomorphisms and flows. During the late 1950s and the early 1960s, Maurício Peixoto...
Anosovdiffeomorphisms by Yakov Sinai who used the symbolic model to construct Gibbs measures. In the early 1970s the theory was extended to Anosov flows...
{\displaystyle 6g-6} -dimensional closed ball. A diffeomorphism S → S {\displaystyle S\to S} is called pseudo-Anosov if there exists two transverse measured foliations...
properties. The study of pseudo-Anosovdiffeomorphisms of a surface is fundamental. They are the most interesting diffeomorphisms, since finite-order mapping...
pseudorandom number generators (PRNG) and is based on Anosov C-systems (Anosovdiffeomorphism) and Kolmogorov K-systems (Kolmogorov automorphism). It...
Alexandroff compactification and the Alexandrov topology Dmitri Anosov, developed Anosovdiffeomorphism Vladimir Arnold, an author of the Kolmogorov–Arnold–Moser...
Alexandroff compactification and the Alexandrov topology Dmitri Anosov, developed Anosovdiffeomorphism Vladimir Arnold, an author of the Kolmogorov–Arnold–Moser...
Alexandroff compactification and the Alexandrov topology Dmitri Anosov, developed Anosovdiffeomorphism Vladimir Arnold, an author of the Kolmogorov–Arnold–Moser...
Fractal Limit set Lyapunov exponent Orbit Periodic point Phase space Anosovdiffeomorphism Arnold tongue axiom A dynamical system Bifurcation diagram Box-counting...
solvmanifolds that are not nilmanifolds. The mapping torus of an Anosovdiffeomorphism of the n-torus is a solvmanifold. For n = 2 {\displaystyle n=2}...
3-manifold that fibers over the circle and whose monodromy is a pseudo-Anosovdiffeomorphism, then the interior of M has a complete hyperbolic metric of finite...
pp. 299–302. Bowen: Equilibrium States and the Ergodic Theory of AnosovDiffeomorphisms. (Lecture Notes in Mathematics, no. 470: A. Dold and B. Eckmann...
expansion to the classification of dynamical systems by showing that Anosovdiffeomorphisms exist on many manifolds of high dimension. F. T. Farrell, L. E....
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