80 research outputs found
Multifractal analysis of Lyapunov exponent for the backward continued fraction map
In this note we study the multifractal spectrum of Lyapunov exponents for
interval maps with infinitely many branches and a parabolic fixed point. It
turns out that, in strong contrast with the hyperbolic case, the domain of the
spectrum is unbounded and points of non-differentiability might exist.
Moreover, the spectrum is not concave. We establish conditions that ensure the
existence of inflection points. We also study the thermodynamic formalism for
such maps. We prove that the pressure function is real analytic in a certain
interval and then it becomes equal to zero
Thermodynamic formalism for the positive geodesic flow on the modular surface
In this note we study the thermodynamic formalism for the positive geodesic
flow on the modular surface. We define the pressure and prove the variational
principle. We also establish conditions for the the pressure to be real
analytic and for the potentials to have unique equilibrium states. The results
in this paper were largely superceded by "Phase transitions for suspension
flows" by Iommi and Jordan arXiv:1202.0849Comment: This note is not intended for publication. It was largely superceded
by the paper "Phase transitions for suspension flows" by Iommi and Jordan,
arXiv:1202.084
An elementary non-recursive expression for the partition function P(n)
Consideration of a classification of the number of partitions of a natural
number according to the members of sub-partitions differing from unity leads to
a non-recursive formula for the number of irreducible representations of the
symmetric group Sn. This article was published, long ago, under the title A
non-recursive expression for the number of irreducible representations of the
Symmetric Group Sn, Physica 114A, 1982, 361-364, North-Holland Publishing Co.
The Introduction has been, somewhat, improved, however, the handmade result
remains unproved.Comment: 5 pages, 2 figure
Branching rules for the Weyl Groups of the Unitary and Orthogonal Lie Groups
This note presents a procedure to determine the reduction of the irreducible
and the induced characters of the symmetric group in terms of the irreducible
and induced characters of the hyperoctahedral group
Key Words: Symmetric Group, Hyperoctahedral group, Representations,
Characters, Re- duction.Comment: 14 page
Symbolic Languages and Ars Combinatoria
This article analyses some paragraphs of the Dissertatio de Arte Combinatoria
(1666) where G.W. Leibniz considers the syntax of a language with a given
number of primitive terms. We propose a new formulation which generalizes the
philosopher conception of such a formal system.Comment: 10 pages, 2 figure
Thermodynamic formalism for interval maps: inducing schemes
This survey article concerns inducing schemes in the context of interval
maps. We explain how the study of these induced systems allows for the fine
description of, not only, the thermodynamic formalism for certain multimodal
maps, but also of its multifractal structure.Comment: Surve
Zero temperature limits of Gibbs states for almost-additive potentials
This paper is devoted to study ergodic optimisation problems for
almost-additive sequences of functions (rather than a fixed potential) defined
over countable Markov shifts (that is a non-compact space). Under certain
assumptions we prove that any accumulation point of a family of Gibbs
equilibrium measures is a maximising measure. Applications are given in the
study of the joint spectral radius and to multifractal analysis of Lyapunov
exponent of non-conformal maps.Comment: Changes in Sections 4 and 5 are included in this versio
Transience in Dynamical Systems
We extend the theory of transience to general dynamical systems with no
Markov structure assumed. This is linked to the theory of phase transitions. We
also provide examples of new kinds of transient behaviour.Comment: Changes have been made mostly in Sections 1 and
Time change for flows and thermodynamic formalism
This paper is devoted to study how do thermodynamic formalism quantities
varies for time changes of suspension flows defined over countable Markov
shifts. We prove that in general no quantity is preserved. We also make a
topological description of the space of suspension flows according to certain
thermodynamic quantities. For example, we show that the set of suspension flows
defined over the full shift on a countable alphabet having finite entropy is
open. Of independent interest might be a set of analytic tools we use to
construct examples with prescribed thermodynamic behaviour
Pressure, Poincar\'e series and box dimension of the boundary
In this note we prove two related results. First, we show that for certain
Markov interval maps with infinitely many branches the upper box dimension of
the boundary can be read from the pressure of the geometric potential.
Secondly, we prove that the box dimension of the set of iterates of a point in
H^n with respect to a parabolic subgroup of isometries equals the critical
exponent of the Poincare series of the associated group. This establishes a
relationship between the entropy at infinity and dimension theory.Comment: Introduction has been rewritten. Comments welcom
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