694,133 research outputs found

### Sato-Crutchfield formulation for some Evolutionary Games

The Sato-Crutchfield equations are studied analytically and numerically. The
Sato-Crutchfield formulation is corresponding to losing memory. Then
Sato-Crutchfield formulation is applied for some different types of games
including hawk-dove, prisoner's dilemma and the battle of the sexes games. The
Sato-Crutchfield formulation is found not to affect the evolutionarily stable
strategy of the ordinary games. But choosing a strategy becomes purely random
independent on the previous experiences, initial conditions, and the rules of
the game itself. Sato-Crutchfield formulation for the prisoner's dilemma game
can be considered as a theoretical explanation for the existence of cooperation
in a population of defectors.Comment: 9 pages, 3 figures, accepted for Int. J. Mod. Phys.

### On a class of reductions of Manakov-Santini hierarchy connected with the interpolating system

Using Lax-Sato formulation of Manakov-Santini hierarchy, we introduce a class
of reductions, such that zero order reduction of this class corresponds to dKP
hierarchy, and the first order reduction gives the hierarchy associated with
the interpolating system introduced by Dunajski. We present Lax-Sato form of
reduced hierarchy for the interpolating system and also for the reduction of
arbitrary order. Similar to dKP hierarchy, Lax-Sato equations for $L$ (Lax
fuction) due to the reduction split from Lax-Sato equations for $M$ (Orlov
function), and the reduced hierarchy for arbitrary order of reduction is
defined by Lax-Sato equations for $L$ only. Characterization of the class of
reductions in terms of the dressing data is given. We also consider a waterbag
reduction of the interpolating system hierarchy, which defines
(1+1)-dimensional systems of hydrodynamic type.Comment: 15 pages, revised and extended, characterization of the class of
reductions in terms of the dressing data is give

### Sato-Tate distributions of twists of y^2=x^5-x and y^2=x^6+1

We determine the limiting distribution of the normalized Euler factors of an
abelian surface A defined over a number field k when A is isogenous to the
square of an elliptic curve defined over k with complex multiplication. As an
application, we prove the Sato-Tate Conjecture for Jacobians of Q-twists of the
curves y^2=x^5-x and y^2=x^6+1, which give rise to 18 of the 34 possibilities
for the Sato-Tate group of an abelian surface defined over Q. With twists of
these two curves one encounters, in fact, all of the 18 possibilities for the
Sato-Tate group of an abelian surface that is isogenous to the square of an
elliptic curve with complex multiplication. Key to these results is the
twisting Sato-Tate group of a curve, which we introduce in order to study the
effect of twisting on the Sato-Tate group of its Jacobian.Comment: minor edits, 42 page

### Motivic Serre group, algebraic Sato-Tate group and Sato-Tate conjecture

We make explicit Serre's generalization of the Sato-Tate conjecture for
motives, by expressing the construction in terms of fiber functors from the
motivic category of absolute Hodge cycles into a suitable category of Hodge
structures of odd weight. This extends the case of abelian varietes, which we
treated in a previous paper. That description was used by
Fite--Kedlaya--Rotger--Sutherland to classify Sato-Tate groups of abelian
surfaces; the present description is used by Fite--Kedlaya--Sutherland to make
a similar classification for certain motives of weight 3. We also give
conditions under which verification of the Sato-Tate conjecture reduces to the
identity connected component of the corresponding Sato-Tate group.Comment: 34 pages; restriction to odd weight adde

### Sato-Tate groups of some weight 3 motives

We establish the group-theoretic classification of Sato-Tate groups of
self-dual motives of weight 3 with rational coefficients and Hodge numbers
h^{3,0} = h^{2,1} = h^{1,2} = h^{0,3} = 1. We then describe families of motives
that realize some of these Sato-Tate groups, and provide numerical evidence
supporting equidistribution. One of these families arises in the middle
cohomology of certain Calabi-Yau threefolds appearing in the Dwork quintic
pencil; for motives in this family, our evidence suggests that the Sato-Tate
group is always equal to the full unitary symplectic group USp(4).Comment: Minor edits to correct typos and address LMFDB modular form label
change

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