Dynamical system (definition) and Function (mathematics)

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Difference between Dynamical system (definition) and Function (mathematics)

Dynamical system (definition) vs. Function (mathematics)

The dynamical system concept is a mathematical formalization for any fixed "rule" which describes the time dependence of a point's position in its ambient space. In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

Compact space

In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).

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Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

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Differentiable function

In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.

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Differential equation

A differential equation is a mathematical equation that relates some function with its derivatives.

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Empty set

In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.

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Functional (mathematics)

In mathematics, the term functional (as a noun) has at least two meanings.

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Graph of a function

In mathematics, the graph of a function f is, formally, the set of all ordered pairs, and, in practice, the graphical representation of this set.

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Image (mathematics)

In mathematics, an image is the subset of a function's codomain which is the output of the function from a subset of its domain.

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Integer

An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

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Interval (mathematics)

In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.

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Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Ordinary differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

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Tuple

In mathematics, a tuple is a finite ordered list (sequence) of elements.

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Vector field

In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.

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