This article is about a property of dynamical systems. For the property of arithmetical semigroups, see Abstract analytic number theory. For the axiom for posets, see Baumgartner's axiom.
In mathematics, Smale's axiom A defines a class of dynamical systems which have been extensively studied and whose dynamics is relatively well understood. A prominent example is the Smale horseshoe map. The term "axiom A" originates with Stephen Smale.[1][2] The importance of such systems is demonstrated by the chaotic hypothesis, which states that, 'for all practical purposes', a many-body thermostatted system is approximated by an Anosov system.[3]
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments...
Smale's axiomA defines a class of dynamical systems which have been extensively studied and whose dynamics is relatively well understood. A prominent...
mathematics, the axiom of choice, abbreviated AC or AoC, is an axiom of set theory equivalent to the statement that a Cartesian product of a collection of...
Axiom Space, Inc., also known as Axiom Space, is an American privately funded space infrastructure developer headquartered in Houston, Texas. Founded in...
mathematical logic, the Peano axioms (/piˈɑːnoʊ/, [peˈaːno]), also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers...
Axiom of extensionality Axiom of empty set Axiom of pairing Axiom of union Axiom of infinity Axiom schema of replacement Axiom of power set Axiom of...
Axiom Orbital Segment or Axiom Segment (or AxS) are the planned modular components of the International Space Station (ISS) designed by Houston, Texas...
set theory, the axiom schema of specification, also known as the axiom schema of separation (Aussonderung Axiom), subset axiom or axiom schema of restricted...
the axiom of infinity is one of the axioms of Zermelo–Fraenkel set theory. It guarantees the existence of at least one infinite set, namely a set containing...
The Isuzu Axiom is a mid-size SUV introduced by Isuzu in 2001 for the 2002 model year. The Axiom is derived from the Isuzu Rodeo and was intended to be...
theory (with or without the axiom of choice) is still the best-known and most studied. Set theory is commonly employed as a foundational system for the...
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the axiom of regularity (also known as the axiom of foundation) is an axiom of Zermelo–Fraenkel set theory that states that every non-empty set A contains...
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probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. These axioms remain central...
In mathematics, an axiom of countability is a property of certain mathematical objects that asserts the existence of a countable set with certain properties...
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mathematical logic, an axiom schema (plural: axiom schemata or axiom schemas) generalizes the notion of axiom. An axiom schema is a formula in the metalanguage...
An action axiom is an axiom that embodies a criterion for describing action. Action axioms are of the form "If a condition holds, then the following will...
computer science that use it, the axiom of extensionality, axiom of extension, or axiom of extent, is one of the axioms of Zermelo–Fraenkel set theory....
Axiom Telecom is a technology retailer founded in 1997 by Faisal Al Bannai, with four employees at the start of its operations. Axiom became the official...
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