Beyond the periodic orbit theory

Predrag Cvitanović, Kim Hansen, Juri Rolf, G. Vattay

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The global constraints on chaotic dynamics induced by the analyticity of smooth flows are used to dispense with individual periodic orbits and derive infinite families of exact sum rules for several simple dynamical systems. The associated Fredholm determinants are of particularly simple polynomial form. The theory developed suggests an alternative to the conventional periodic orbit theory approach for determining eigenspectra of transfer operators.

Original languageEnglish
Pages (from-to)1209-1232
Number of pages24
JournalNonlinearity
Volume11
Issue number5
DOIs
Publication statusPublished - Sep 1998

Fingerprint

Periodic Orbits
Orbits
Fredholm Determinant
orbits
Global Constraints
Transfer Operator
Sum Rules
Chaotic Dynamics
Analyticity
determinants
dynamical systems
sum rules
Dynamical systems
polynomials
Dynamical system
Polynomials
operators
Polynomial
Alternatives
Form

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Cvitanović, P., Hansen, K., Rolf, J., & Vattay, G. (1998). Beyond the periodic orbit theory. Nonlinearity, 11(5), 1209-1232. https://doi.org/10.1088/0951-7715/11/5/003

Beyond the periodic orbit theory. / Cvitanović, Predrag; Hansen, Kim; Rolf, Juri; Vattay, G.

In: Nonlinearity, Vol. 11, No. 5, 09.1998, p. 1209-1232.

Research output: Contribution to journalArticle

Cvitanović, P, Hansen, K, Rolf, J & Vattay, G 1998, 'Beyond the periodic orbit theory', Nonlinearity, vol. 11, no. 5, pp. 1209-1232. https://doi.org/10.1088/0951-7715/11/5/003
Cvitanović, Predrag ; Hansen, Kim ; Rolf, Juri ; Vattay, G. / Beyond the periodic orbit theory. In: Nonlinearity. 1998 ; Vol. 11, No. 5. pp. 1209-1232.
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