Abstract
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.
Refences
A. Lasota and M. Mackey,Probabilistic properties of Deterministic Systems (Cambridge University Press, Cambridge, 1985).
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).
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).
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 β-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).
D. J. Driebe and G. E. Ordóñez, Using symmetries of the Frobenius-Perron operator to determine spectral decompositions,Phys. Lett. A 211:204 (1996).
P. A. M. Dirac,The Principles of Quantum Mechanics (Oxford University Press, London, 1958).
M. Abramowitz and I. A. Stegun, eds.Handbook of Mathematical Functions (Dover, Publications New York, 1972).
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Communicated by J. L. Lebowitz
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Ordóñez, G.E., Driebe, D.J. Spectral decomposition of tent maps using symmetry considerations. J Stat Phys 84, 269–276 (1996). https://doi.org/10.1007/BF02179586
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DOI: https://doi.org/10.1007/BF02179586