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A transfer orbit is used by spacecraft to move between two different orbits, often described by the Hohmann transfer orbit which is an energy-efficient path.

A stable orbit is one where nearby trajectories remain close to the orbit over time, implying future behavior remains predictable.

A quasi-periodic orbit is characterized by motion on a torus in phase space, with frequencies that are incommensurate, leading to non-repeating trajectories that fill the torus.

A homoclinic orbit connects a critical point with itself in phase space, potentially indicating complex, chaotic behavior in dynamical systems.

A heteroclinic orbit connects different critical points or equilibria in phase space. Its presence indicates the system's transitions between different states.

A periodic orbit repeats its path in phase space after a fixed period, showing a regular, cyclic behavior in a dynamical system.

A chaotic orbit displays sensitive dependence on initial conditions, leading to unpredictability and a trajectory that appears random in a deterministic system.

An unstable orbit is such that nearby trajectories diverge away from the orbit over time, making future behavior increasingly unpredictable.

A Lyapunov orbit exists near equilibrium points in the vicinity of gravitational bodies, where the gravitational pull and centrifugal force balance each other.