<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Let G be the group generated by z ↦ z+2 and z → -1/z , z ∈ ℂ. This group acts on the upper half plane and the associated quotient surface is topologically a sphere with two cusps. Assigning a “geometric” code to an oriented geodesic not going to cusps, with alphabets in ℤ \ {0}, enables us to conjugate the geodesic ow on this surface to a special ow over the symbolic space of these geometric codes. We will show that for k ≥ 1, a subsystem with codes from ℤ \ {0; ±1; ±2;… ; ±k} is a TBS: topologically Bernouli scheme. For similar codes for geodesic ow on modular surface, this was true for k ≥ 3. We also give bounds for the entropy of these subsystems. </p></abstract>

Let G be the group generated by z ↦ z+2 and z → -1/z , z ∈ ℂ. This group acts on the upper half plane and the associated quotient surface is topologically a sphere with two cusps. Assigning a “geometric” code to an oriented geodesic not going to cusps, with alphabets in ℤ \ {0}, enables us to conjugate the geodesic ow on this surface to a special ow over the symbolic space of these geometric codes. We will show that for k ≥ 1, a subsystem with codes from ℤ \ {0; ±1; ±2;… ; ±k} is a TBS: topologically Bernouli scheme. For similar codes for geodesic ow on modular surface, this was true for k ≥ 3. We also give bounds for the entropy of these subsystems.

Geodesic Flow on the Quotient Space of the Action of ⟨z + 2;−1/z 〉 on the Upper Half Plane

University of Guilan, Faculty of Mathematics

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Let G be the group generated by z ↦ z+2 and z → -1/z , z ∈ ℂ. This group acts on the upper half plane and the associated quotient surface is topologically a...

Geodesic Flow on the Quotient Space of the Action of ⟨z + 2;−1/z 〉 on the Upper Half Plane

Publié en ligne: 21 mai 2013

Pages: 37 - 50

DOI: https://doi.org/10.2478/v10309-012-0054-z

Mots clés
geodesic ow, geometric code, arithmetic code, topological entropy

This content is open access.

Geodesic Flow on the Quotient Space of the Action of ⟨z + 2;−1/z 〉 on the Upper Half Plane

Publié en ligne: 21 mai 2013

Pages: 37 - 50

DOI: https://doi.org/10.2478/v10309-012-0054-z

Mots clésgeodesic ow, geometric code, arithmetic code, topological entropy

This content is open access.

Mots clés
geodesic ow, geometric code, arithmetic code, topological entropy