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Symbolic dynamics originated as a method to study general dynamical systems; now its techniques and ideas have found significant applications in data storage and transmission, linear algebra, the motions of the planets and many other areas [citation needed]. The distinct feature in symbolic dynamics is that time is measured in discrete intervals.
A symbolic flow or subshift is a closed T-invariant subset Y of X [3] and the associated language L Y is the set of finite subsequences of Y. [ 4 ] Now let A be an n × n adjacency matrix with entries in {0, 1}.
Pages in category "Symbolic dynamics" The following 8 pages are in this category, out of 8 total. This list may not reflect recent changes. ...
In symbolic dynamics and related branches of mathematics, a shift space or subshift is a set of infinite words that represent the evolution of a discrete system. In fact, shift spaces and symbolic dynamical systems are often considered synonyms. The most widely studied shift spaces are the subshifts of finite type and the sofic shifts.
The symbolic name of x, with regards to the partition Q, is the sequence of integers {a n} such that T n x ∈ Q a n . {\displaystyle T^{n}x\in Q_{a_{n}}.} The set of symbolic names with respect to a partition is called the symbolic dynamics of the dynamical system.
The horseshoe map was designed to reproduce the chaotic dynamics of a flow in the neighborhood of a given periodic orbit. The neighborhood is chosen to be a small disk perpendicular to the orbit . As the system evolves, points in this disk remain close to the given periodic orbit, tracing out orbits that eventually intersect the disk once again.
This is a list of dynamical system and differential equation topics, by Wikipedia page. See also list of partial differential equation topics , list of equations . Dynamical systems, in general
The mathematical disciplines of combinatorics and dynamical systems interact in a number of ways. The ergodic theory of dynamical systems has recently been used to prove combinatorial theorems about number theory which has given rise to the field of arithmetic combinatorics.