Typical properties of periodic Teichmüller geodesics: Lyapunov exponents

2021 ◽  
pp. 1-29
Author(s):  
URSULA HAMENSTÄDT
Keyword(s):  
Growth Rate ◽  
Vector Bundle ◽  
Lyapunov Exponents ◽  
Periodic Orbits ◽  
Moduli Space ◽  
Abelian Differentials ◽  
The Matrix ◽  
Teichmüller Flow

Abstract Consider a component ${\cal Q}$ of a stratum in the moduli space of area-one abelian differentials on a surface of genus g. Call a property ${\cal P}$ for periodic orbits of the Teichmüller flow on ${\cal Q}$ typical if the growth rate of orbits with property ${\cal P}$ is maximal. We show that the following property is typical. Given a continuous integrable cocycle over the Teichmüller flow with values in a vector bundle $V\to {\cal Q}$ , the logarithms of the eigenvalues of the matrix defined by the cocycle and the orbit are arbitrarily close to the Lyapunov exponents of the cocycle for the Masur–Veech measure.

scholarly journals A large deviations bound for the Teichmüller flow on the moduli space of abelian differentials

2010 ◽  
Vol 31 (4) ◽  
pp. 1043-1071 ◽  
Author(s):  
VÍTOR ARAÚJO ◽  
ALEXANDER I. BUFETOV
Keyword(s):  
Dynamical Systems ◽  
Large Deviations ◽  
Moduli Space ◽  
Geodesic Flow ◽  
Large Deviation ◽  
Suspension Flows ◽  
Abelian Differentials ◽  
Quantitative Recurrence ◽  
Teichmuller Geodesic Flow ◽  
Teichmüller Flow

AbstractLarge deviation rates are obtained for suspension flows over symbolic dynamical systems with a countable alphabet. We use a method employed previously by the first author [Large deviations bound for semiflows over a non-uniformly expanding base. Bull. Braz. Math. Soc. (N.S.)38(3) (2007), 335–376], which follows that of Young [Some large deviation results for dynamical systems. Trans. Amer. Math. Soc.318(2) (1990), 525–543]. As a corollary of the main results, we obtain a large deviation bound for the Teichmüller flow on the moduli space of abelian differentials, extending earlier work of Athreya [Quantitative recurrence and large deviations for Teichmuller geodesic flow. Geom. Dedicata119 (2006), 121–140].

Correlations for Interaction Layer Growth in U-Mo/Al Dispersion Fuels

2017 ◽  
Vol 375 ◽  
pp. 29-39
Author(s):  
Boris A. Tarasov ◽  
Stepan N. Nikitin ◽  
Dmitry P. Shornikov ◽  
Maria S. Tarasova ◽  
Igor I. Konovalov
Keyword(s):  
Growth Rate ◽  
Growth Process ◽  
Aluminum Matrix ◽  
Layer Growth ◽  
Radiation Diffusion ◽  
Fission Rate ◽  
Interaction Layer ◽  
The Matrix ◽  
Mechanism And Kinetics ◽  
Kinetics Of

Paper presents the results of the growth rate of the interaction layer of uranium-molybdenum dispersed fuel in aluminum matrix and influence of silicon alloying on it. The growth process of amorphous interaction layer depends on the radiation diffusion which is proportional to the fission rate in the power of 1⁄4. The alloying of the matrix by silicon does not lead to a change in the mechanism and kinetics of the interaction layer growth, but only slows it down.

scholarly journals Algebraic independence of multipliers of periodic orbits in the space of polynomial maps of one variable

2014 ◽  
Vol 36 (4) ◽  
pp. 1156-1166 ◽  
Author(s):  
IGORS GORBOVICKIS
Keyword(s):  
Periodic Orbits ◽  
Moduli Space ◽  
Algebraic Independence ◽  
Complex Polynomials ◽  
Generic Point ◽  
Algebraic Functions ◽  
Polynomial Maps ◽  
Affine Subspaces

We consider the space of complex polynomials of degree $n\geq 3$ with $n-1$ distinct marked periodic orbits of given periods. We prove that this space is irreducible and the multipliers of the marked periodic orbits, considered as algebraic functions on that space, are algebraically independent over $\mathbb{C}$. Equivalently, this means that at its generic point the moduli space of degree-$n$ polynomial maps can be locally parameterized by the multipliers of $n-1$ arbitrary distinct periodic orbits. We also prove a similar result for a certain class of affine subspaces of the space of complex polynomials of degree $n$.

On the integrability of intermediate distributions for Anosov diffeomorphisms

1995 ◽  
Vol 15 (2) ◽  
pp. 317-331 ◽  
Author(s):  
M. Jiang ◽  
Ya B. Pesin ◽  
R. de la Llave
Keyword(s):  
Finite Number ◽  
Lyapunov Exponents ◽  
Periodic Orbits ◽  
Three Dimensional ◽  
Dimensional Torus ◽  
Anosov Diffeomorphism ◽  
Anosov Diffeomorphisms ◽  
Stable Foliation

AbstractWe study the integrability of intermediate distributions for Anosov diffeomorphisms and provide an example of a C∞-Anosov diffeomorphism on a three-dimensional torus whose intermediate stable foliation has leaves that admit only a finite number of derivatives. We also show that this phenomenon is quite abundant. In dimension four or higher this can happen even if the Lyapunov exponents at periodic orbits are constant.

Effect of Two-Stage Aging on Microstructure and Properties of Al-Mg-Si Alloys

2022 ◽  
Vol 905 ◽  
pp. 51-55
Author(s):  
Li Wang ◽  
Ya Ya Zheng ◽  
Shi Hu Hu
Keyword(s):  
Growth Rate ◽  
Grain Boundary ◽  
Tensile Properties ◽  
Tensile Testing ◽  
Diffusion Rate ◽  
Two Stage ◽  
Precipitated Phase ◽  
Transmission Electron ◽  
The Matrix ◽  
Microstructure Characteristic

The effects of two-stage aging on the microstructures, tensile properties and intergranular corrosion (IGC) sensitivity of Al-Mg-Si alloys were studied by tensile testing and IGC experiments and transmission electron microscope (TEM). The results show that the two-stage aging (180°C, 2h+160°C, 120h) can reduce the IGC sensitivity without decrease the tensile properties. The grain is distributed with high-density β′′ phases, and the grain boundary phases are spherical and intermittently distributed. The formation of the microstructure characteristic is due to the lower re-aging temperature, which results in a decline differences in the diffusion rate between the matrix and grain boundaries. As a result, the pre-precipitated phase can maintain a better strengthening effects due to the slower growth rate. The pre-precipitated phase of the grain boundary presents a spherical and intermittent distribution due to the fast coarsening speed.

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