Publicación: EXPANSIVITY IN 2-METRIC SPACES
Fecha
2015
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INDIAN JOURNAL OF MTHEMATICS
Resumen
WE STUDY THE NOTION OF EXPANSIVITY FOR BOTH HOMEOMORPHISMS AND MEASURES ON 2-METRIC SPACES [8]. AT FIRST GLANCE WE SHOW THAT THERE ARE INFINITE COMPACT CONTINUOUS 2-METRIC SPACES EXHIBITING EXPANSIVE HOMEOMORPHISMS IN THE 2-METRIC SENSE (ROUGHLY SPEAKING 2-METRIC EXPANSIVE HOMEOMORPHISMS). NEXT WE PROVE THE ABSENCE OF EXPANSIVE MEASURES IN THE 2-METRIC SENSE (OR 2-METRIC EXPANSIVE MEASURES) FOR HOMEOMORPHISMS OF SK (K = 1,2) EQUIPPED WITH THE STANDARD TRIANGLE-AREA A INDUCED BY RK+1. WE THEN CONCLUDE THAT THERE ARE NO 2-METRIC EXPANSIVE HOMEOMORPHISMS OF (SK,A) FOR K = 1,2. FINALLY, IT IS PROVED THAT THE SET OF THE SET OF HETEROCLINIC POINTS FOR 2-METRIC EXPANSIVE HOMEOMORPHISMS ON COMPACT CONTINUOUS 2-METRIC SPACES IS COUNTABLE. THIS EXTENDS A WELL-KNOWN RESULT BY REDDY [19].
