separatrix Definition
- 1a curve or surface that separates two parts of a space or object
- 2a line or boundary that separates two different types of things
Using separatrix: Examples
Take a moment to familiarize yourself with how "separatrix" can be used in various situations through the following examples!
Example
The separatrix between the two colors was very distinct.
Example
The separatrix of the room was a curtain.
Example
The separatrix between the two classes was the final exam.
separatrix Synonyms and Antonyms
Synonyms for separatrix
- boundary
- partition
- divider
- demarcation
- dividing line
Phrases with separatrix
a curve or surface in phase space that separates trajectories of a Hamiltonian system
Example
The separatrix of the pendulum is a curve that separates the oscillating motion from the rotating motion.
separatrix of a PDE
a curve or surface that separates regions of different solutions to a partial differential equation
Example
The separatrix of the heat equation separates the regions of the initial temperature distribution that will eventually converge to zero and those that will not.
a theorem in mathematics that states that a smooth vector field on a compact manifold has a finite number of limit cycles, which are separated by invariant curves called separatrix
Example
The separatrix theorem is an important result in the study of dynamical systems.
Summary: separatrix in Brief
A 'separatrix' [sep-uh-rey-triks] is a curve or surface that divides two parts of a space or object. It can also refer to a line or boundary that separates two different types of things. Examples include the separatrix between two colors, the separatrix of a room, and the separatrix between two classes. In mathematics, it can refer to the separatrix of a Hamiltonian system, the separatrix of a PDE, or the separatrix theorem.
