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Prodotti recenti

The Hopf–Rinow theorem and the Mañé critical value for magnetic geodesics on odd-dimensional spheres

The subject of this article are magnetic geodesics on odd-dimensional spheres endowed with the round metric and with the magnetic potential given by the standard contact form. We compute the Mañé critical value of the system and show that a value of the energy is supercritical if and only if all pairs of points on the sphere can be connected by a magnetic geodesic with that value of the energy. Our methods are explicit and rely on the description of the submanifolds invariant by the flow and ...

Symplectic capacities of domains close to the ball and Banach–Mazur geodesics in the space of contact forms

We prove that all normalized symplectic capacities coincide on smooth domains in Cn which are C 2-close to the Euclidean ball, whereas this fails for some smooth domains which are just C 1-close to the ball. We also prove that all symplectic capacities whose value on ellipsoids agrees with that of the nth Ekeland–Hofer capacity coincide in a C 2-neighborhood of the Euclidean ball of Cn. These results are deduced from a general theorem about contact forms which are C 2-close to Zoll ones, sayi...

The multiplicity problem for periodic orbits of magnetic flows on the 2-sphere

We consider magnetic Tonelli Hamiltonian systems on the cotangent bundle of the 2-sphere, where the magnetic form is not necessarily exact. It is known that, on very low and on high energy levels, these systems may have only finitely many periodic orbits. Our main result asserts that almost all energy levels in a precisely characterized intermediate range (e0,e1) possess infinitely many periodic orbits. Such a range of energies is non-empty, for instance, in the physically relevant case where...

Configurational entropy of randomly double-folding ring polymers

Topologically constrained genome-like polymers often double-fold into tree-like configurations. Here, we calculate the exact number of tightly double-folded configurations available to a ring polymer in ideal conditions. For this purpose, we introduce a scheme that allows us to define a “code” specifying how a ring wraps a randomly branching tree and calculate the number of admissible wrapping codes via a variant of Bertrand’s ballot theorem. As a validation, we demonstrate that data from Mon...

Configurational entropy of random trees

We present a graph theoretical approach to the configurational statistics of random treelike objects, such as randomly branching polymers. In particular, for ideal trees we show that Prüfer labeling provides (i) direct access to the exact configurational entropy as a function of the tree composition, (ii) computable exact expressions for partition functions and important experimental observables for tree ensembles with controlled branching activity, and (iii) an efficient sampling scheme for ...

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Collections: [14696] Home page macrotipologia

Prodotti recenti

The Hopf–Rinow theorem and the Mañé critical value for magnetic geodesics on odd-dimensional spheres

Symplectic capacities of domains close to the ball and Banach–Mazur geodesics in the space of contact forms

The multiplicity problem for periodic orbits of magnetic flows on the 2-sphere

Configurational entropy of randomly double-folding ring polymers

Configurational entropy of random trees

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SISSA DIGITAL LIBRARYInstitutional Research Information System (Statistiche: prodotti, OA)Per informazioni contatta [email protected]

Collections: [14696] Home page macrotipologia

Prodotti recenti

The Hopf–Rinow theorem and the Mañé critical value for magnetic geodesics on odd-dimensional spheres

Symplectic capacities of domains close to the ball and Banach–Mazur geodesics in the space of contact forms

The multiplicity problem for periodic orbits of magnetic flows on the 2-sphere

Configurational entropy of randomly double-folding ring polymers

Configurational entropy of random trees

Scopri

Tipologia

Autore

Data di pubblicazione

Editore

Rivista

Serie

Settore disciplinare

Keyword

Lingua

Accesso al fulltext

SISSA DIGITAL LIBRARYInstitutional Research Information System (Statistiche: prodotti, OA)
Per informazioni contatta [email protected]