135) Directional derivatives and the central limit theorem on compact general one-dimensional lattices,

joint work with V. Vargas, preprint (2024)

134) Idempotent approach to level-2 variational principles in Thermodynamical Formalism,

joint work with J. K. Mengue and E. R. Oliveira, preprint (2024)

133) The Dirac operator for the pair of Ruelle and Koopman operators and a generalized Boson formalism

joint work with William M. M. Braucks , preprint (2024)

132) Parametrized Families of Gibbs Measures and their Statistical Inference

joint work with M. Denker, M. Kessebohmer and S. R. C. Lopes, preprint (2024)

131) Thermodynamic Formalism for a family of cellular automata and duality with the shift

joint work with Elismar R. Oliveira and Marcelo Sobottka, preprint (2024)

130) "Noncommutative integration, quantum mechanics, Tannaka's theorem for compact groupoids and examples"

joint work with M. Sebastiani and V. Vargas

preprint (2023)

129) "Grand-canonical Thermodynamic Formalism via IFS: volume, temperature, gas pressure and grand-canonical topological pressure"

joint work with E. R. Oliveira, W. A. de S. Pedra and V. Vargas

128) "Geodesics and dynamical information projections on the manifold of Holder equilibrium probabilities",

joint work with Rafael Ruggiero, to appear in Stoch. and Dynamics.

127) "The sectional curvature of the infinite dimensional manifold of Holder equilibrium probabilities"

joint work with R. Ruggiero, to appear in Proc. of the Edinburg Matematical Soc.

126) Level-2 IFS Thermodynamic Formalism: Gibbs probabilities in the space of probabilities and the push-forward map

joint work with Elismar R. Oliveira, Dyn. Systems, Volume 39, - Issue 4, 823-847 (2024)

125) "Diffusion Processes: entropy, Gibbs states and the continuous time Ruelle operator",

joint work with G. Muller, and A. Neumann

Journal of Dynamics and Games, Vol. 12, No. 2, pp. 105-117 (2025)

124) "Thermodynamic Formalism on the Skhorohd space: the continuous time Ruelle operator, entropy, pressure, entropy production and expansiveness"

joint work with J. Knorst, G. Muller, and A. Neumann

Sao Paulo Journal of Math. Sciences, 18:1414-1446 (2024)

123) "Spectral Triples on Thermodynamic Formalism and Dixmier Trace Representations of Gibbs Measures: theory and examples"

joint work with L. Cioletti, L. Hataishi and M. Stadlbauert

Nonlinearity, Volume 37, Number 10, 105010 (56pp) (2024)

122) On the quantum Guerra-Morato Action Functional

joint work with J. Knorst, Journ. of Math. Physics 65, issue 8, 082102 (2024)

121) "The generalized IFS Bayesian method and an associated variational principle covering the classical and dynamical cases"

joint work with J. K. Mengue

Dyn. Systems, VOL. 39, NO. 2, 206-230 (2024)

120) "Thermodynamic formalism for continuous-time quantum Markov semigroups: the detailed balance condition, entropy, pressure and equilibrium quantum processes",

joint work with Jader E. Brasil and Josue Knorst

Open Systems and Information Dynamics, Volume 30, Issue 04 2350018 (13 pages) (2023)

119) " Parameter estimation in Manneville-Pomeau processes"

joint work with B. Olbermann and S. R. C. Lopes

Probability, Uncertainty and Quantitative Risk, Vol. 8, No. 2, 213-234 (2023)

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118) "Explicit Bivariate Rate Functions for Large Deviations in AR(1) and MA(1) Processes with Gaussian Innovations"

joint work with M. Karling and S. R. C. Lopes

Probability, Uncertainty and Quantitative Risk, Vol. 8, No. 2, 177-212 (2023)

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117) "Thermodynamic Formalism for Quantum Channels: Entropy, Pressure, Gibbs Channels and generic properties"

joint work with Jader Brasil and Josue Knorst,

Communications in Contemporary Mathematics, Volume 25, Issue 04, 2150090 (2023)

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116) "Dynamical hypothesis tests and Decision Theory for Gibbs distributions",

joint work with M. Denker and S. R. C. Lopes

Discrete and Continuous Dynamical Systems - Series A - Vol. 43, No. 5, pp. 1942-1958 (2023)

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115) "The involution kernel and the dual potential for functions in the Walters family",

joint work with Lucas Y. Hataishi, Qualitative Theory of Dynamical Systems, 22- Article 26 (2023)

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114) "Entropy, pressure, ground states and calibrated sub-actions for linear dynamics",

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Bull. of the Braz. Math. Soc. 53:1073-1106 (2022)

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113) "On information gain, Kullback-Leibler divergence, entropy production and the involution kernel"

joint work Jairo Mengue

Disc. and Cont. Dyn. Syst. Series A, Vol. 42, No. 7, 3593-3627 (2022)

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112) "Decision Theory and Large Deviations for Dynamical hypotheses tests: the Neyman-Pearson Lemma, Min-Max and Bayesian Tests"

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Journal of Dynamics and Games, Volume 9, Number 2, April 2022 - pp 125-150

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111) "Bayes posterior convergence for loss functions via almost additive Thermodynamic Formalism"

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Journ. of Statis. Physics, 186:35 (2022)

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110) "Pentadiagonal Matrices and an Application to the Centered MA(1) Stationary Gaussian Process",

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International Journal of Applied Mathematics and Statistics, Vol. 61; Issue No. 1, pp 1-22 (2022)

109) "Nonequilibrium in Thermodynamic Formalism: the Second Law, gases and Information Geometry"

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Qualitative Theory of Dynamical Systems 21: 21 p 1-44 (2022) MR4356488

108) "Lyapunov exponents for Quantum Channels: an entropy formula and generic properties"

joint work Jader E. Brasil, and Josue Knorst

Journal of Dynamical Systems and Geometric Theories, Vol 19(2) 155-187 (2021) MR4358481

107) "Invariant probabilities for discrete time Linear Dynamics via Thermodynamic Formalism"

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Nonlinearity 34 (2021) 8359-8391 MR4344719

106) "An iterative process for approximating subactions"

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Modeling, Dynamics, Optimization and Bioeconomics IV" Editors: Alberto Pinto and David Zilberman, Springer Proceedings in Mathematics and Statistics, Springer Verlag, pp 187--212 (2021)

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105) "On Bertelson-Gromov Dynamical Morse Entropy ",

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"Modeling, Dynamics, Optimization and Bioeconomics IV" Editors: Alberto Pinto and David Zilberman, Springer Proceedings in Mathematics and Statistics, Springer Verlag, 297--321, (2021)

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104) "Haar systems, KMS states on von Neumann algebras and C^*-algebras on dynamically defined groupoids and Noncommutative Integration"

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103) "Thermodynamic Formalism for Haar systems in Noncommutative Integration: transverse functions and entropy of transverse measures"

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Erg. Theo. and Dyn. Systems, (2021), 41, 1835-1863 MR4252210

102) "Quantum Spin probabilities at positive temperature are Holder Gibbs probabilities"

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Comm. in Contemporary Mathematics Vol. 23, No. 1 (2021) 1950050 (32 pages) MR4169241

101) "Explicit examples in Ergodic Optimization"

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Sao Paulo Journal of Math. Sciences - Vol 14 - pp 443-489 (2020) MR4173468

100) "The Ruelle operator for symmetric beta-shifts"

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Publicacions Mathematiques, 661 - 680 - Volume 64, Issue 2 (2020) MR4119264

99) "Gibbs States and Gibbsian Specifications on the space R^N"

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Dyn. Systems., Volume 35, Issue 2, 216-241 (2020) MR4120828

98) "Ruelle Operator for Continuous Potentials and DLR-Gibbs Measures",

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Disc and .Cont. Dyn. Syst. A Vol 40, N. 8, 4625-4652 (2020) MR4112024

97) "Correlation Inequalities and Monotonicity Properties of the Ruelle Operator",

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Stoch. and Dyn, 19 (2019), no. 6, 1950048, 31 pp MR4033007

96) "Continuous groupoids on the symbolic space, quasi-invariant probabilities for Haar systems and the Haar-Ruelle operator"

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Bull of the Braz. Math. Soc., Vol 50. Issue 3, pp 663-683 (2019) MR3993188

95) "The KMS Condition for the homoclinic equivalence relation and Gibbs probabilities",

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Sao Paulo Journ. of Math. Sciences, Volume 13, Issue 1, pp 248-282 (2019) MR3947403

94) "A general renormalization procedure on the one-dimensional lattice and decay of correlations",

Stoch. and Dyn., Vol. 19, No. 01, 1950003 (2019) MR3904031

93) "The calculus of thermodynamical formalism",

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Journ. of the European Math Society, Vol 20, Issue 10, pages 2357-2412 (2018) MR3852182

92) "Large Deviations for Quantum Spin probabilities at temperature zero",

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Stochastics and Dynamics, Vol. 18, No. 06, 1850044 (2018) MR3869882

91) "Selection of calibrated subaction when temperature goes to zero in the discounted problem",

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90) "A formula for the Entropy of the Convolution of Gibbs probabilities on the circle",

Nonlinearity, 31 , 3441-3459 (2018) MR3816762

89) "Uma breve Introducao a Matematica da Mecanica Quantica"

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88) "Introducao a Matematica da Mecanica Quantica"

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87) "On the thin boundary of the fat attractor"

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"Modeling, Dynamics, Optimization and Bioeconomics III" Editors: Alberto Pinto and David Zilberman, Springer Proceedings in Mathematics and Statistics, Springer Verlag, 205-246 (2018) MR3806667

86) "Transport and large deviations for Schrodinger operators and Mather measures",

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85) "An introduction to Coupling"

"Modeling, Dynamics, Optimization and Bioeconomics II" Editors: Alberto Pinto and David Zilberman, Springer Proceedings in Mathematics and Statistics, pp 307-335, (2017) Springer Verlag MR3718407

84) "A detailed proof of the von Neumann's Quantum Ergodic Theorem",

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Quantum Studies: Mathematics and Foundations - Vol 4 - Issue 3, 263-285 (2017) MR3692490

83) "Interactions, Specifications, DLR probabilities and the Ruelle Operator in the One-Dimensional Lattice"

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82) "Spectral Properties of the Ruelle Operator for Product Type Potentials on Shift Spaces",

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81) "Semiclassical limits, Lagrangian states and coboundary equations",

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80) "Duality between Eigenfunctions and Eigendistributions of Ruelle and Koopman operators via an integral kernel"

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79) "Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps",

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Nonlinearity, 28, Number 11, 4117-4137 (2015) MR3424906

78) "Generic properties for random repeated quantum iterations",

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Quantum Studies: Mathematics and Foundations, Vol 2, pp 389-402 (2015) MR3412580

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76) " Entropy and Variational Principle for one-dimensional Lattice Systems with a general a-priori probability: positive and zero temperature"

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75) "The Dual Potential, the involution kernel and Transport in Ergodic Optimization"

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74) "Phase Transitions in One-dimensional Translation Invariant Systems: a Ruelle Operator Approach"

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73) "Large Deviations for stationary probabilities of a family of continuous time Markov chains via Aubry-Mather theory"

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72) "On generic G-prevalent properties and a quantitative K-S theorem for C^{r} diffeomorphisms of the circle"

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Dynamical Systems: an Int. Journ. Vol 30. Issue 1, 1-12 (2015) MR3304972

71) "Ergodic Transport Theory, periodic maximizing probabilities and the twist condition"

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"Modeling, Optimization, Dynamics and Bioeconomy I", Springer Proceedings in Mathematics and Statistics, Volume 73, Edit. David Zilberman and Alberto Pinto, 183-219 (2014) MR3297616

70) "Selection of measure and a Large Deviation Principle for the general one-dimensional XY model"

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Dyn. Systems: an Int. Jour. Vol 29, Issue 1 (2014) pp 24-39 MR3170635

69) "On the selection of subaction and measure for a subclass of potentials defined by P. Walters"

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Erg. Theo. and Dyn. Systems, Volume 33, issue 05, pp. 1338--1362 (2013) MR3103086

68) "Ergodic Optimization, Zero Temperature Limits and the Max-Plus Algebra"

joint work with A. Baraviera and R. Leplaideur, mini-course in XXIX Coloquio Brasileiro de Matematica (2013) MR3114331

67) "A thermodynamic formalism for continuous time Markov chains with values on the Bernoulli Space: entropy, pressure and large deviations"

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66) "The effective potential and transshipment in thermodynamic formalism at temperature zero"

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65) "Ergodic Transport Theory and Piecewise Analytic Subactions for Analytic Dynamics"

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Bull. of the Braz. Math Soc. Vol 43 (3) 467-512 (2012) MR3024067

64) "Duality Theorems in Ergodic Transport"

joint work with J. Mengue, Journal of Statistical Physics. Vol 149, issue 5, pp 921-942 (2012) MR2999567

63) "Wigner measures and the semi-classical limit to the Aubry-Mather measure"

joint work with Diogo Gomes and Joana Mohr,

Applied Mathematics Research Express, Volume 2012, Issue 2, 152-183 (2012) MR2982772

62) "The potential point of view for renormalization",

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Stochastic and Dynamics, Vol 12. N 4, (2012) 1250005(1-34) MR2990585

61) "Selection of ground states in the zero temperature limit for a one-parameter family of potentials"

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SIAM Journal on Applied Dynamical Systems, Vol. 11, n 1, 243-260 (2012) MR2902616

60) "On the general one-dimensional XY Model: positive and zero temperature, selection and non-selection"

joint work with A. T. Baraviera, L. M. Cioletti, J. Mohr, R. R. Souza,

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59) "A dynamical point of view of Quantum Information: Wigner measures",

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Dynamics, Games and Science II, DYNA 2008, Edit. M. Peixoto, A. Pinto and D Rand, pp 161-186 Springer Verlag (2011) MR2883277

58) "A dynamical point of view of Quantum Information: entropy and pressure",

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57) "Large deviations and Aubry-Mather measures supported in nonhyperbolic closed geodesics"

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56) "The Mather measure and a Large Deviation Principle for the Entropy Penalized Method",

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55) "Quantum Stochastic Processes, Quantum Iterated Function Systems and Entropy"

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54) "Zeta measures and Thermodynamic Formalism for temperature zero"

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53) "A Thermodynamic Formalism for density matrices in Quantum Information",

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Applied Mathematics Research Express, Vol. 2010, No. 1, pp. 63-118 (2010) MR2629875

52) "Poncelet pairs and the Twist Map associated to the Poncelet Billiard",

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50) "Minimax Probabilities for Aubry-Mather problems",

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49) "On calibrated and separating sub-actions",

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48) "Entropy and variational principles for holonomic probabilities of IFS",

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47) "KMS States, Entropy and a Variational Principle for Pressure",

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46) " Negative Entropy, Zero temperature and stationary Markov chains on the interval",

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45) "C*- Algebras and Thermodynamic Formalism",

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44) "Exponential decay of correlation for the Stochastic Process associated to the Entropy Penalized Method",

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43) "Eigenfunctions of the Laplacian and associated Ruelle operator ",

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42) "On the Aubry-Mather theory for symbolic dynamics",

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39) "A Large Deviation Principle for the equilibrium states of Holder Potentials: the zero temperature case",

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31) `` The capacity costfunction of a hard constrained channel"

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29)"On the minimal action function of an autonomous Lagrangian associated with a magnetic phenomena"

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