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A fractal is a complex geometric shape that can be split into parts, each of which is a reduced-scale copy of the whole, commonly seen in chaotic dynamic systems.

An attractor is a set of numerical values toward which a system tends to evolve for a wide variety of starting conditions.

An equilibrium point is a steady-state solution to a dynamic system where all variables remain constant.

Topological mixing is a property in dynamical systems where, in the course of time, the system evolves in such a way that any given region or open set eventually overlaps with any other given region.

A bifurcation occurs when a small smooth change made to the parameter values of a system causes a sudden 'qualitative' or topological change in its behavior.

Lyapunov exponents measure the rate of separation of infinitesimally close trajectories in a dynamic system, determining the rate of chaos.

Nonlinear dynamics studies systems that are governed by equations more complex than a simple linear relationship, leading to rich and often unpredictable behavior.

Phase space is a multidimensional space in which all possible states of a dynamic system are represented, with each state corresponding to one unique point in the phase space.

Chaos theory deals with dynamic systems that are highly sensitive to initial conditions, making long-term predictions impossible.

A dynamic system is a system, described by a set of rules, that models how variables change over time or space.

A limit cycle is a closed trajectory in phase space that a system can oscillate around in a periodic fashion.