Introduction to the Modern Theory of Dynamical Systems

Katok, A., & Boris Hasselblatt, I. t. t. M. T. o. D. S. (1995). Introduction to the Modern Theory of Dynamical Systems. Cambridge University Press.

Type

Book

Intellectual base

Textbook

Year

1995

Link

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Cited by

4 citations across 4 artifacts.

Domain-specific

• Denjoy's theorem on rotation number
  • … or diffeomorphism regularity, positive derivative, bounded-variation hypothesis, irrational rotation number, topological conjugacy, orbit density, and counterexample boundary are explicit. to An applied instance preserves the same invariant under a changed scale, notation, jurisdiction, dataset, or implementation..
• Rational dependence
  • The coefficient field is specifically the rationals, zero coefficients are allowed but not all may vanish, dependence of numbers as vectors over Q differs from algebraic dependence by polynomial relations and pairwise irrational ratios do not guarantee larger-set independence.
• Recurrent point
  • … observable transfers from An irrational rotation of the circle makes every point recurrent: its orbit never repeats exactly but returns arbitrarily close to its starting location. to A compact dynamical model uses the recurrent set and its closure to separate persistent orbit behavior from transient regions..
• Rotation number
  • … that the circle orientation, homeomorphism or map class, lift convention, iterate limit, independence from initial point, modulo-one identification, and regularity assumptions are explicit. to An applied instance preserves the same invariant under a changed scale, notation, jurisdiction, dataset, or implementation..

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