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  2. List of chaotic maps - Wikipedia

    en.wikipedia.org/wiki/List_of_chaotic_maps

    Download as PDF; Printable version; ... Chaotic maps often occur in the study of dynamical systems. ... 2D Lorenz system [1] discrete: real: 2: 1:

  3. Sharkovskii's theorem - Wikipedia

    en.wikipedia.org/wiki/Sharkovskii's_theorem

    Sharkovskii's theorem does not immediately apply to dynamical systems on other topological spaces. It is easy to find a circle map with periodic points of period 3 only: take a rotation by 120 degrees, for example. But some generalizations are possible, typically involving the mapping class group of the space minus a periodic orbit.

  4. Dynamical system - Wikipedia

    en.wikipedia.org/wiki/Dynamical_system

    A discrete dynamical system, discrete-time dynamical system is a tuple (T, M, Φ), where M is a manifold locally diffeomorphic to a Banach space, and Φ is a function. When T is taken to be the integers, it is a cascade or a map. If T is restricted to the non-negative integers we call the system a semi-cascade. [14]

  5. Dynamical systems theory - Wikipedia

    en.wikipedia.org/wiki/Dynamical_systems_theory

    Dynamical systems theory and chaos theory deal with the long-term qualitative behavior of dynamical systems.Here, the focus is not on finding precise solutions to the equations defining the dynamical system (which is often hopeless), but rather to answer questions like "Will the system settle down to a steady state in the long term, and if so, what are the possible steady states?", or "Does ...

  6. Logistic map - Wikipedia

    en.wikipedia.org/wiki/Logistic_map

    The concept of fixed points is of primary importance in discrete dynamical systems. Another graphical technique that can be used for one-variable mappings is the spider web projection. After determining an initial value x 0 {\displaystyle x_{0}} on the horizontal axis, draw a vertical line from the initial value x 0 {\displaystyle x_{0}} to the ...

  7. Random dynamical system - Wikipedia

    en.wikipedia.org/wiki/Random_dynamical_system

    In the mathematical field of dynamical systems, a random dynamical system is a dynamical system in which the equations of motion have an element of randomness to them. Random dynamical systems are characterized by a state space S, a set of maps from S into itself that can be thought of as the set of all possible equations of motion, and a probability distribution Q on the set that represents ...

  8. Symbolic dynamics - Wikipedia

    en.wikipedia.org/wiki/Symbolic_dynamics

    In mathematics, symbolic dynamics is the study of dynamical systems defined on a discrete space consisting of infinite sequences of abstract symbols. The evolution of the dynamical system is defined as a simple shift of the sequence. Because of their explicit, discrete nature, such systems are often relatively easy to characterize and understand.

  9. Orbit (dynamics) - Wikipedia

    en.wikipedia.org/wiki/Orbit_(dynamics)

    In mathematics, specifically in the study of dynamical systems, an orbit is a collection of points related by the evolution function of the dynamical system. It can be understood as the subset of phase space covered by the trajectory of the dynamical system under a particular set of initial conditions, as the system evolves.