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Axiom A

Known as: Axiom A diffeomorphism, Axiom A system, Morse–Smale diffeomorphism 
In mathematics, Smale's axiom A defines a class of dynamical systems which have been extensively studied and whose dynamics is relatively well… 
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Highly Cited
2015
Highly Cited
2015
A bstractRecently it has been established that torsional Newton-Cartan (TNC) geometry is the appropriate geometrical framework to… 
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Review
2011
Review
2011
Research is reviewed on the identification and construction of physical systems with chaotic dynamics due to uniformly hyperbolic… 
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2010
2010
We show that the Lipschitz shadowing property of a diffeomorphism is equivalent to structural stability. As a corollary, we show… 
Highly Cited
2008
Highly Cited
2008
We analyse some properties of the cohomogeneity one Ricci soliton equations, and use Ansätze of cohomogeneity one to produce new… 
Highly Cited
1999
Highly Cited
1999
Given a dynamical system and a function f from the state space to the real numbers, an optimal orbit for f is an orbit over which… 
Highly Cited
1993
Highly Cited
1993
The Geometry of Exponential Families. Calculus on Manifolds. Statistical Manifolds. Connections. Curvature. Information Metrices… 
Highly Cited
1993
Highly Cited
1993
This paper deals with the dynamics of a simple family of holomorphic diffeomorphisms of $\C^2$: the polynomial automorphisms… 
Highly Cited
1992
Highly Cited
1992
We prove exponential decay of correlations for (f, μ), wheref belongs in a positive measure set of quadratic maps of the interval… 
Review
1989
Review
1989
Letf:X↦X be an expanding map of a compact space (small distances are increased by a factor >1). A generating functionζ(z) is… 
Highly Cited
1969
Highly Cited
1969
In [7] S. Smale poses the problem of classifying all Anosov diffeomorphisms of compact manifolds up to topological conjugacy. The…