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Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, often referred to as the "butterfly effect." Describe the principles of chaos theory, including key concepts such as sensitive dependence on initial conditions, attractors, and bifurcations. Discuss how chaos theory applies to classical mechanics and provide examples of chaotic systems. Evaluate the implications of chaos theory for predicting long-term behavior in physical systems and its impact on our understanding of determinism.
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