Scholarpedia: Phase Space
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Peer-reviewed encyclopedia article explaining phase space as the set of all possible states of a dynamical system. It covers trajectories, flows, phase portraits and the Hamiltonian setting, so readers can interpret system behavior geometrically rather than through individual solutions.
More resources on Phase Spaces
ChaosBook.org
Free graduate-level online textbook led by Predrag Cvitanović at Georgia Tech, with accompanying video lectures. It develops periodic-orbit theory and cycle expansions, teaching readers to compute averages, escape rates and spectra of chaotic deterministic and quantum systems from their unstable periodic orbits.
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Differential Equations, Dynamical Systems, and an Introduction to Chaos (3rd Edition)
Proof-based successor to Hirsch and Smale's classic, building phase space theory from linear systems and canonical forms through nonlinear flows, equilibria and stability, limit sets, the Poincare-Bendixson theorem, bifurcations, and chaotic attractors, with exercises.
Linear Phase Portraits: Matrix Entry (MIT Mathlets)
Browser applet for homogeneous linear autonomous systems: set the four entries of a two-by-two matrix and watch the phase portrait redraw while eigenvalues and the trace-determinant point move, showing when trajectories become saddles, nodes, spirals or centers.
Qualitative Behavior: Phase Portraits (MIT 18.03SC)
Covers sketching trajectories of two-dimensional linear systems in the phase plane, classifying critical points as nodes, saddles, spirals or centers, and reading stability from the trace-determinant diagram. Includes notes, problem-solving videos, Mathlet demonstrations and practice problems with solutions, so learners can sketch portraits unaided.