Michiko Yuri |

Faculty of Science Mathematics Mathematics |

Specially Appointed Professor |

Last Updated :2020/09/10

- - Tsuda College Faculty of Liberal Arts
- - Tsuda College Graduate School of Mathematics and Computer Science
- - Tsuda College Faculty of Arts and Science
- - Tsuda College Graduate School, Division of Natural Science

- Cambridge University Press 1998
**Dynamical Systems and Ergodic Theory(共著)** - Cambridge University Press 1998
**Dynamical Systems and Ergodic Theory(共著)**

- M Yuri COMMUNICATIONS IN MATHEMATICAL PHYSICS 241- (2-3) 453 -466 2003/10 [Not refereed][Not invited]

In this paper, we associate weak Gibbs measures for intermittent maps with non-Gibbsian weakly Gibbsian states in statistical mechanics in the sense of Dobrushin [4, 5]. We show a higher dimensional intermittent map of which the Sinai-Bowen-Ruelle measure is a weak Gibbs equilibrium state and a weakly Gibbsian state in the sense of Dobrushin admitting essential discontinuities in its conditional probabilities. - Communications in Mathematical Physics (241) 453 -466 2003 [Not refereed][Not invited]
**Weak Gibbs measares for Internittent Systems and Weakly Gibbsian States in Statis tical Mechanics** - Transactions of the American Mathematical Society 355- (7) 2949 -2971 2003 [Not refereed][Not invited]
- Communications in Mathematical Physics (241) 453 -466 2003 [Not refereed][Not invited]
**Weak Gibbs measares for Internittent Systems and Weakly Gibbsian States in Statis tical Mechanics** - Transactions of the American Mathematical Society 355- (7) 2949 -2971 2003 [Not refereed][Not invited]
- Transactions of the American Mathematical Society 355- (7) 2949 -2971 2003 [Not refereed][Not invited]
- M Yuri ERGODIC THEORY AND DYNAMICAL SYSTEMS 22- (22) 1933 -1955 2002/12 [Not refereed][Not invited]

We establish a version of the local product structure (weak local product structure) for ergodic measures (mu) over bar which are the invertible extension of ergodic weak Gibbs measures mu invariant under piecewise C-0-invertible (infinite to one) Markov maps T. As a special case, (mu) over bar possesses asymptotically 'almost' local product structure in the sense of Barreira, Pesin and Schmeling. Under piecewise conformality of T and the existence of a piecewise smooth representation of the dual map of T, the weak local product structure allows one to show that the pointwise dimension of (mu) over bar exists almost everywhere and is the sum of the pointwise dimension of mu, and the pointwise dimension of the dual of mu. Our results can be applicable to a natural extension of piecewise conformal two-dimensional Markov map which is related to a complex continued fraction and admits indifferent periodic points. - Michiko Yuri Ergodic Theory and Dynamical Systems 22- (6) 1933 -1955 2002/12 [Not refereed][Not invited]

We establish a version of the local product structure (weak local product structure) for ergodic measures μ̄ which are the invertible extension of ergodic weak Gibbs measures μ invariant under piecewise C0-invertible (infinite to one) Markov maps T. As a special case, μ̄ possesses asymptotically 'Almost' local product structure in the sense of Barreira, Pesin and Schmeling. Under piecewise conformality of T and the existence of a piecewise smooth representation of the dual map of T, the weak local product structure allows one to show that the pointwise dimension of μ̄ exists almost everywhere and is the sum of the pointwise dimension of μ and the pointwise dimension of the dual of μ. Our results can be applicable to a natural extension of piecewise conformal two-dimensional Markov map which is related to a complex continued fraction and admits indifferent periodic points. - M Yuri COMMUNICATIONS IN MATHEMATICAL PHYSICS 230- (2) 365 -388 2002/10 [Not refereed][Not invited]

In this paper, we establish a multifractal formalism of weak Gibbs measures associated to potentials of weak bounded variation for certain nonhyperbolic systems. We apply our results to Manneville-Pomeau type maps and a piecewise conformal two-dimensional countable Markov map with indifferent periodic points which is related to a complex continued fraction. - Michiko Yuri Communications in Mathematical Physics 230- (2) 365 -388 2002/10 [Not refereed][Not invited]

In this paper, we establish a multifractal formalism of weak Gibbs measures associated to potentials of weak bounded variation for certain nonhyperbolic systems. We apply our results to Manneville-Pomeau type maps and a piecewise conformal two-dimensional countable Markov map with indifferent periodic points which is related to a complex continued fraction. - M Yuri NONLINEARITY 15- (2) 429 -445 2002/03 [Not refereed][Not invited]

We shall clarify the speed of L-1-convergence of iterated transfer operators and rates of decay of correlations for multi-dimensional noninvertible maps with indifferent periodic points related to a class of functions which contains all piecewise Lipschitz functions. The essential issue for solving these problems is to clarify the speed of uniform convergence of transfer operators on compact sets excluding indifferent periodic points. Our results can be applicable to higher dimensional countable to one intermittent maps for which previous techniques on decay of correlations do not work. - Ergodic Theory and Dynamical Systems (Cambridge University) (22) 1933 -1955 2002 [Not refereed][Not invited]
- Nonlinearity 15- (2) 429 -445 2002 [Not refereed][Not invited]
- Commanications in mathematical Physics 230- (2) 365 -388 2002 [Not refereed][Not invited]
- Nonlinearity 15- (2) 429 -445 2002 [Not refereed][Not invited]
- M Pollicott, M Yuri NONLINEARITY 14- (5) 1265 -1278 2001/09 [Not refereed][Not invited]

In this paper we study the meromorphic domains of zeta functions for multidimensional maps with indifferent period points. This partially extends known results for certain one-dimensional transformations. Our method involves deriving, in a natural way, a uniformly hyperbolic map and relating the zeta functions for these two transformations. - M Pollicott, M Yuri NONLINEARITY 14- (5) 1265 -1278 2001/09 [Not refereed][Not invited]

In this paper we study the meromorphic domains of zeta functions for multidimensional maps with indifferent period points. This partially extends known results for certain one-dimensional transformations. Our method involves deriving, in a natural way, a uniformly hyperbolic map and relating the zeta functions for these two transformations. - Mark Pollicott, Michiko Yuri Nonlinearity 14- (5) 1265 -1278 2001/09 [Not refereed][Not invited]

In this paper we study the meromorphic domains of zeta functions for multi-dimensional maps with indifferent period points. This partially extends known results for certain one-dimensional transformations. Our method involves deriving, in a natural way, a uniformly hyperbolic map and relating the zeta functions for these two transformations. - M Pollicott, M Yuri COMMUNICATIONS IN MATHEMATICAL PHYSICS 217- (3) 503 -520 2001/03 [Not refereed][Not invited]

In this note we present an axiomatic approach to the decay of correlations for maps of arbitrary dimension with indifferent periodic points. As applications, we apply our results to the well-known Manneville-Pomeau equation and the inhomogeneous diophantine approximation algorithm. - M Pollicott, M Yuri COMMUNICATIONS IN MATHEMATICAL PHYSICS 217- (3) 503 -520 2001/03 [Not refereed][Not invited]

In this note we present an axiomatic approach to the decay of correlations for maps of arbitrary dimension with indifferent periodic points. As applications, we apply our results to the well-known Manneville-Pomeau equation and the inhomogeneous diophantine approximation algorithm. - M Yuri ERGODIC THEORY AND DYNAMICAL SYSTEMS 20- (5) 1495 -1518 2000/10 [Not refereed][Not invited]
**Weak Gibbs measures for certain non-hyperbolic systems**

We study a weak Gibbs property of equilibrium states for potentials of weak bounded variation and for maps admitting indifferent periodic points. We further establish statistical properties of the weak Gibbs measures and bounds of their pointwise dimension. We apply our results to higher-dimensional maps (which are not necessarily conformal) with indifferent periodic points and show that their absolutely continuous finite invariant measures are weak Gibbs measures. - Colloquium Mathematicum(Polish Academy of Science) 84-85- 377 -383 2000 [Not refereed][Not invited]
**A note on the construction of nonsingular Gibbs measures(共著)** - M Yuri TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 352- (5) 2369 -2388 2000 [Not refereed][Not invited]
**Statistical properties for nonhyperbolic maps with finite range structure**

We establish the central limit theorem and non-central limit theorems for maps admitting indifferent periodic points (the so-called intermittent maps). We also give a large class of Darling-Kac sets for intermittent maps admitting infinite invariant measures. The essential issue for the central limit theorem is to clarify the speed of L-1-convergence of iterated Perron-Frobenius operators for multi-dimensional maps which satisfy Renyi's condition but fail to satisfy the uniformly expanding property. Multi-dimensional intermittent maps typically admit such derived systems. There are examples in section 4 to which previous results on the central limit theorem are not applicable, but our extended central limit theorem does apply. - Ergodic Theory and Dynamical Systems(Cambridge University Press) 20- (5) 1495 -1518 2000 [Not refereed][Not invited]
**Weak Gibbs measures for certain nonhyperbolic systems** - Colloquium Mathematicum(Polish Academy of Science) 84-85- 377 -383 2000 [Not refereed][Not invited]
**A note on the construction of nonsingular Gibbs measures(共著)** - Transactions of the American Mathematical Society 352- (5) 2369 -2388 2000 [Not refereed][Not invited]
**Statistical properties for nonhyperbolic maps with finite range structure** - M Yuri ERGODIC THEORY AND DYNAMICAL SYSTEMS 19- (5) 1365 -1378 1999/10 [Not refereed][Not invited]
**Thermodynamic formalism for certain nonhyperbolic maps**

We establish a generalized thermodynamic formalism for certain nonhyperbolic maps with countably many preimages. We study-existence and uniqueness of conformal measures and statistical properties of the equilibrium states absolutely continuous with respect to the conformal measures. We will see that such measures are not Gibbs but satisfy a version of Gibbs property (weak Gibbs measure). We apply our results to a one-parameter family of one-dimensional maps and a two-dimensional nonconformal map related to number theory. Both of them admit indifferent periodic points. - Transactions of the American Mathematical Society 351- (2) 559 -568 1999 [Not refereed][Not invited]
**Regularity of solutions to the measurable Livsic equation(共著 : with M.Pollicott)** - Ergodic Theory and Dynamical Systems 19- (5) 1365 -1378 1999 [Not refereed][Not invited]
**Thermodynamic Formalism for certain nonhyperbolic maps** - Transactions of the American Mathematical Society 351- (2) 559 -568 1999 [Not refereed][Not invited]
**Regularity of solutions to the measurable Livsic equation(共著 : with M.Pollicott)** - M Yuri ERGODIC THEORY AND DYNAMICAL SYSTEMS 18- (6) 1589 -1612 1998/12 [Not refereed][Not invited]
**Zeta functions for certain non-hyperbolic systems and topological Markov approximations**

We study dynamical (Artin-Mazur-Ruelle) zeta functions for piecewise invertible multi-dimensional maps. In particular, we direct our attention to nonhyperbolic systems admitting countable generating definite partitions which are not necessarily Markov but satisfy the finite range structure (FRS) condition. We define a version of Gibbs measure tweak Gibbs measure) and by using it we establish an analogy with thermodynamic formalism for specific cases, i.e. a characterization of the radius of convergence in terms of pressure. The FRS condition leads us to nice countable state symbolic dynamics and allows us to realize it as towers over Markov systems. The Markov approximation method then gives a product formula of zeta functions for certain weighted functions. - POLLICOTT M, SHARP R, YURI M Nonlinearity 11- (4) 1173 -1184 1998 [Not refereed][Not invited]
- Ergodic Theory and Dynamical Systems 18- (6) 1589 -1612 1998 [Not refereed][Not invited]
**Zeta functions for certain nonhyperbolic systems and topological Markov approximations** - Nonlinearity 11- (4) 1173 -1184 1998 [Not refereed][Not invited]
- M Yuri ERGODIC THEORY AND DYNAMICAL SYSTEMS 17- (4) 977 -1000 1997/08 [Not refereed][Not invited]
**On the convergence to equilibrium states for certain non-hyperbolic systems**

We study the convergence to equilibrium states for certain non-hyperbolic piecewise invertible systems. The multi-dimensional maps we shall consider do not satisfy Renyi's condition (uniformly bounded distortion for any iterates) and do not necessarily satisfy the Markov property. The failure of both conditions may cause singularities of densities of the invariant measures, even if they are finite, and causes a crucial difficulty in applying the standard technique of the Perron-Frobenius operator. Typical examples of maps we consider admit indifferent periodic orbits and arise in many contexts. For the convergence of iterates of the Perron-Frobenius operator, we study continuity of the invariant density. - Ergodic Theory and Dynamical Systems 17- (4) 977 -1000 1997 [Not refereed][Not invited]
**On the convergence to equilibrium states for certain nonhyperbolic systems** - M Yuri NONLINEARITY 9- (6) 1439 -1461 1996/11 [Not refereed][Not invited]

We study the decay of correlations for certain multi-dimensional noninvertible maps which do not necessarily satisfy Renyi's condition (the bounded distortion property) and do not necessarily satisfy the Markov condition on the definite partitions. Our method is based on the technique of Markov approximations which was developed by Chernov. We relate the slowness of the; decay of correlations to the singularity of the invariant density which is caused by the lack of hyperbolicity. We also see that it can be described by the distortion property of the distributions of the invariant densities. - Nonlinearity 9- (6) 1439 -1461 1996 [Not refereed][Not invited]
- M YURI INDAGATIONES MATHEMATICAE-NEW SERIES 6- (3) 355 -383 1995/09 [Not refereed][Not invited]
**MULTIDIMENSIONAL MAPS WITH INFINITE INVARIANT-MEASURES AND COUNTABLE STATE SOFIC SHIFTS**

We study multi-dimensional maps on bounded domains of R(d) satisfying the finite range structure (FRS) condition, which leads us to countable state sofic systems. Such maps admit sigma-finite ergodic invariant measures equivalent to Lebesgue measures under the local Renyi condition. In this paper we show that several ergodic properties still hold even if such invariant measures are infinite. We also investigate the validity of Rohlin's entropy formula and of a variational principle for entropy. - Indagationes Mathematicae 6- 355 -383 1995 [Not refereed][Not invited]
**Multi-dimensional Maps with infinite invariant measures and countable state sofic shifts** - M YURI NONLINEARITY 7- (3) 1093 -1124 1994/05 [Not refereed][Not invited]

We investigate singular points of the invariant density foe a class of multi-dimensional maps with finite range structure. In particular, we concentrate on maps with infinitely many discontinuity points which do not satisfy Renyi's condition and do not necessarily satisfy the Markov property. Such maps occur in many contexts. Under some conditions. we show that indifferent periodic points must be singular points of the invariant density. - Nonlinearity 7- (3) 1093 -1124 1994 [Not refereed][Not invited]
- Shunji Ito, Michiko Yuri Tokyo Journal of Mathematics 10- (1) 1 -32 1987 [Not refereed][Not invited]
- Shunji Ito, Michiko Yuri Tokyo Journal of Mathematics 10- (1) 1 -32 1987 [Not refereed][Not invited]
- Michiko Yuri Tokyo Journal of Mathematics 9- (2) 457 -485 1986 [Not refereed][Not invited]
- Tokyo Journal of Mathematics 9- 457 -485 1986 [Not refereed][Not invited]
**On a Bernoulli property for multi-dimensional maps with finite range structure** - Michiko Yuri Tokyo Journal of Mathematics 6- (2) 291 -296 1983 [Not refereed][Not invited]
- Tokyo Journal of Mathematics 6- 291 -296 1983 [Not refereed][Not invited]
**A construction of an invariant foliation by the shadowing lemma** - Israel Journal of Mathematics 131, 221-257- [Not refereed][Not invited]
**Pressures and equilibrium states for countable Markov Shifts** - Israel Journal of Mathematics 131, 221-257- [Not refereed][Not invited]
**Pressures and equilibrium states for countable Markov Shifts**

- Date (from‐to) : 2005 -2006
**複雑系におけるギブス性の崩壊と相転移現象** **Phase transition and NonGibbsianness for complex systems**