Preface Acknowledgements Part I. One-Dimensional Integrable Systems: 1. Lie groups 2. Lie algebras 3. Factorizations and homogeneous spaces 4. Hamilton's equations and Hamiltonian systems 5. Lax equations 6. Adler-Kostant-Symes 7. Adler-Kostant-Symes (continued) 8. Concluding remarks on one-dimensional Lax equations Part II. Two-Dimensional Integrable Systems: 9. Zero-curvature equations 10. Some solutions of zero-curvature equations 11. Loop groups and loop algebras 12. Factorizations and homogeneous spaces 13. The two-dimensional Toda lattice 14. T-functions and the Bruhat decomposition 15. Solutions of the two-dimensional Toda lattice 16. Harmonic maps from C to a Lie group G 17. Harmonic maps from C to a Lie group (continued) 18. Harmonic maps from C to a symmetric space 19. Harmonic maps from C to a symmetric space (continued) 20. Application: harmonic maps from S2 to CPn 21. Primitive maps 22. Weierstrass formulae for harmonic maps Part III. One-Dimensional and Two-Dimensional Integrable Systems: 23. From 2 Lax equations to 1 zero-curvature equation 24. Harmonic maps of finite type 25. Application: harmonic maps from T2 to S2 26. Epilogue References Index.
Preface Acknowledgements Part I. One-Dimensional Integrable Systems: 1. Lie groups 2. Lie algebras 3. Factorizations and homogeneous spaces 4. Hamilton's equations and Hamiltonian systems 5. Lax equations 6. Adler-Kostant-Symes 7. Adler-Kostant-Symes (continued) 8. Concluding remarks on one-dimensional Lax equations Part II. Two-Dimensional Integrable Systems: 9. Zero-curvature equations 10. Some solutions of zero-curvature equations 11. Loop groups and loop algebras 12. Factorizations and homogeneous spaces 13. The two-dimensional Toda lattice 14. T-functions and the Bruhat decomposition 15. Solutions of the two-dimensional Toda lattice 16. Harmonic maps from C to a Lie group G 17. Harmonic maps from C to a Lie group (continued) 18. Harmonic maps from C to a symmetric space 19. Harmonic maps from C to a symmetric space (continued) 20. Application: harmonic maps from S2 to CPn 21. Primitive maps 22. Weierstrass formulae for harmonic maps Part III. One-Dimensional and Two-Dimensional Integrable Systems: 23. From 2 Lax equations to 1 zero-curvature equation 24. Harmonic maps of finite type 25. Application: harmonic maps from T2 to S2 26. Epilogue References Index.
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