Rigged Hilbert spaces for chaotic dynamical systems

DOI10.1063/1.531703zbMath0860.47013OpenAlexW2063564090MaRDI QIDQ4716493

Oscar F. Bandtlow, Ioannis E. Antoniou, S. Tasaki, Zdzislaw Suchanecki

Publication date: 8 April 1997

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.531703

zbMATH Keywords

inductive limitrigged Hilbert spaceriggingKoopman operatorsRenyi and the baker mapsrigged Hilbert space for the baker maps

Mathematics Subject Classification ID

Linear symmetric and selfadjoint operators (unbounded) (47B25) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70) Dynamical systems and ergodic theory (37-XX)

Related Items

Modern Koopman Theory for Dynamical Systems ⋮ Resonances of dynamical systems and Fredholm-Riesz operators on rigged Hilbert spaces ⋮ Generalized Eigenvalues of the Perron–Frobenius Operators of Symbolic Dynamical Systems ⋮ Dynamic mode decomposition for analytic maps ⋮ New extended spectral decompositions of the Renyi map ⋮ Probabilistic extension and logic of complex unstable dynamical systems ⋮ Eigenfunction expansions and transformation theory ⋮ Extended spectral decompositions of the Rényi map ⋮ Extension of the Dynamics of Unstable Systems

Cites Work

• Spectrum and eigenfunctions of the Frobenius-Perron operator of the tent map
• Generalized spectral decomposition of the \(\beta\)-adic baker's transformation and intrinsic irreversibility
• An extension of the theory of Fredholm determinants
• Meromorphic extensions of generalised zeta functions
• Time-Correlation Functions of One-Dimensional Transformations
• Spectral decomposition of the Renyi map
• Dirac Formalism and Symmetry Problems in Quantum Mechanics. I. General Dirac Formalism