Sur le problème des trois corps et les équations de la dynamique¶
Poincaré, H. (1890). Sur le problème des trois corps et les équations de la dynamique. Acta Mathematica, 13, 1-270.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Eventual Realisation of Possibility
- Statistical physics: Poincaré recurrence — finite isolated systems return arbitrarily close to any prior state given enough time.
This sourceStates the recurrence theorem: a finite isolated dynamical system returns arbitrarily close to any prior state given enough time.
- Statistical physics: Poincaré recurrence — finite isolated systems return arbitrarily close to any prior state given enough time.
- Phase Space
- Conserved quantities are level sets; limit cycles are closed curves; attractors are compact invariant sets; chaos appears as sensitive dependence on initial conditions in the form of positive Lyapunov exponents.
This sourceFoundational result for ergodic theory and the physics of recurrence.
- Conserved quantities are level sets; limit cycles are closed curves; attractors are compact invariant sets; chaos appears as sensitive dependence on initial conditions in the form of positive Lyapunov exponents.
- Recurrence
- Physics & dynamical systems: Poincaré (1890) proved that any isolated, bounded conservative system returns arbitrarily close to its initial state given sufficient time—the recurrence theorem—alongside the modern apparatus of periodic orbits, return times, phase-space trajectories, conservative systems, ergodic theory, and chaos theory with sensitive dependence on initial conditions.
This sourceFoundational result for ergodic theory and the physics of recurrence.
- Physics & dynamical systems: Poincaré (1890) proved that any isolated, bounded conservative system returns arbitrarily close to its initial state given sufficient time—the recurrence theorem—alongside the modern apparatus of periodic orbits, return times, phase-space trajectories, conservative systems, ergodic theory, and chaos theory with sensitive dependence on initial conditions.
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