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Spectral decomposition of tent maps using symmetry considerations. (English) Zbl 1081.37501
Summary: The spectral decomposition of the Frobenius-Perron operator of maps composed of many tents is determined from symmetry considerations. The eigenstates involve Euler as well as Bernoulli polynomials.
##### MSC:
 37A30 Ergodic theorems, spectral theory, Markov operators 37C25 Fixed points, periodic points, fixed-point index theory 37C30 Functional analytic techniques in dynamical systems
##### References:
 [1] A. Lasota and M. Mackey,Probabilistic properties of Deterministic Systems (Cambridge University Press, Cambridge, 1985). [2] W. C. Saphir and H. H. Hasegawa, Spectral representations of the Bernoulli map,Phys. Lett. A 171:317 (1992); H. H. Hasegawa and D. J. Driebe, Spectral determination and physical conditions for a class of chaotic piecewise-linear maps,Phys. Lett. A 176:193 (1993); I. Antoniou and S. Tasaki, Spectral decomposition of the Renyi map,J. Phys. A 26:73 (1993). · doi:10.1016/0375-9601(92)90650-B [3] H. H. Hasegawa and W. C. Saphir, Unitarity and irreversibility in chaotic systems,Phys. Ret. A 46:7401 (1992); P. Gaspard,r-Adic one-dimensional maps and the Euler summation formula,J. Phys. A 25:L483 (1992). · doi:10.1103/PhysRevA.46.7401 [4] H. H. Hasegawa and D. J. Driebe, Intrinsic irreversibility and the validity of the kinetic description of chaotic systems.Phys. Rev. E 50:1781 (1994); I. Antoniou and S. Tasaki, Generalized spectral decomposition of the $\beta$-adic baker’s transformation and intrinsic irreversibility,Physica A 190:303 (1992): I. Antoniou and S. Tasaki, Generalized spectral decompositions of mixing dynamical systems,Int. J. Quantum Chem.46:425 (1993). · doi:10.1103/PhysRevE.50.1781 [5] D. J. Driebe and G. E. Ordóñez, Using symmetries of the Frobenius-Perron operator to determine spectral decompositions,Phys. Lett. A 211:204 (1996). · Zbl 1060.37500 · doi:10.1016/0375-9601(96)00006-0 [6] P. A. M. Dirac,The Principles of Quantum Mechanics (Oxford University Press, London, 1958). [7] M. Abramowitz and I. A. Stegun, eds.Handbook of Mathematical Functions (Dover, Publications New York, 1972).