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A mathematical framework used to model the time-dependent evolution of a point in a geometrical space, often characterized by a set of differential equations.

A set of numerical values toward which a system tends to evolve, regardless of the initial conditions of the system.

An abstract space where all possible states of a system are represented, each state corresponds to one unique point in the phase space.

In dynamical systems, a point in the phase space where the system remains constant or 'fixed' over time.

A process where a symmetrical system results in an asymmetrical outcome during state change, often seen in physics.

A property that is preserved under some transformations, such as rotations or translations, leading to invariant behavior in the dynamics.

A qualitative change in the behavior of a dynamical system, where a small change in a parameter value leads to a sudden topological change in its orbit structure.