Branches of Mathematics
Dynamical Systems
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A dynamical system is the description of how a system evolves in time, under a fixed rule applied to a point in a state space. The branch studies the long-run behaviour of such systems, including their trajectories, stability, periodicity, and chaos, with applications across mathematics, physics, biology, chemistry, engineering, economics, history, and medicine.
Facts
Central QuestionGiven a fixed rule for how a system's state changes from moment to moment, what can be said about its long-run behaviour, stability, periodicity, or unpredictability? 1 Key DebateA fully deterministic dynamical system can still be practically unpredictable. Edward Lorenz summarized the tension this creates for the field: chaos is when the present determines the future but the approximate present does not approximately determine the future. 2 Cross-Tradition Connections
Sources
1. Dynamical System (Wikipedia)
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has applications to a wide variety of fields such as mathematics, physics, biology, chemistry, engineering, economics, history, and medicine
2. Chaos Theory (Wikipedia)
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Chaos: When the present determines the future but the approximate present does not approximately determine the future.
Henri Poincare (Wikipedia)
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In his research on the three-body problem, Poincare became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory.
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