%0 Generic %1 terman2007state %A Terman, David H. %D 2007 %K simulation space state %T State space %U http://www.scholarpedia.org/article/Phase_space %X State space is the set of all possible states of a dynamical system; each state of the system corresponds to a unique point in the state space. For example, the state of an idealized pendulum is uniquely defined by its angle and angular velocity, so the state space is the set of all possible pairs "(angle, velocity)", which form the cylinder S1×R , as in Figure 1. In general, any abstract set could be a state space of some dynamical system. A state space could be finite, consisting of just a few points. It could be finite-dimensional, consisting of an infinite number of points forming a smooth manifold, as usually the case in ordinary differential equations and mappings. Such a state space is often called a phase space. A state space could be infinite-dimensional, as in partial differential equations and delay differential equations. In symbolic dynamics it is a Cantor set, which is zero-dimensional. The number of degrees of freedom of a dynamical system is the dimension of its phase space, i.e., the number of variables the modeler feels is needed to completely describe the system. In the context of Hamiltonian systems, the number of degrees of freedom is the number of pairs of state variables.

@manual{terman2007state, abstract = {State space is the set of all possible states of a dynamical system; each state of the system corresponds to a unique point in the state space. For example, the state of an idealized pendulum is uniquely defined by its angle and angular velocity, so the state space is the set of all possible pairs "(angle, velocity)", which form the cylinder S1×R , as in Figure 1. In general, any abstract set could be a state space of some dynamical system. A state space could be finite, consisting of just a few points. It could be finite-dimensional, consisting of an infinite number of points forming a smooth manifold, as usually the case in ordinary differential equations and mappings. Such a state space is often called a phase space. A state space could be infinite-dimensional, as in partial differential equations and delay differential equations. In symbolic dynamics it is a Cantor set, which is zero-dimensional. The number of degrees of freedom of a dynamical system is the dimension of its phase space, i.e., the number of variables the modeler feels is needed to completely describe the system. In the context of Hamiltonian systems, the number of degrees of freedom is the number of pairs of state variables. }, added-at = {2016-10-05T11:16:00.000+0200}, author = {Terman, David H.}, biburl = {https://www.bibsonomy.org/bibtex/202845375dc9440a6a48b1cd1f7af872f/maanwa}, description = {State space - Scholarpedia}, interhash = {a725e56aaa545aeefb3af05e8f85c60a}, intrahash = {02845375dc9440a6a48b1cd1f7af872f}, keywords = {simulation space state}, timestamp = {2016-10-05T11:16:00.000+0200}, title = {State space}, url = {http://www.scholarpedia.org/article/Phase_space}, year = 2007 }